Similar triangles presentation. Similarity of right triangles. Definition of similar triangles

Collection "Geometry lessons using information technology. Grades 7-9" .
Methodological manual with electronic application / E.M. Savchenko. - M.: Planet, 2011. - 256 p. - (Modern school). ISBN978-5-91658-228-4

This methodological manual is a collection consisting of three parts. The first part of the book presents methods and techniques for using information technology as a mathematics teacher. The second part contains brief annotations and descriptions of digital educational resources that are presented on the disk. The third part is the development of geometry lessons for students in grades 7-9, with a multimedia application for each lesson in the form of presentations. The material meets the requirements of the state educational standard and can be used by teachers working in any curriculum.

The electronic supplement to the book (CD) contains: informative materials for explaining new material, tests, tasks for oral frontal work with students in the classroom. The presented multimedia material will help the teacher make lessons richer, more informative and visual. The CD application can be used when conducting lessons of any type: studying new material, repetition and generalization, in extracurricular work on the subject.

The educational and methodological manual is intended for subject teachers, methodologists, students of advanced training courses for educators, and students of pedagogical universities. .

CONTENT

Part I Using multimedia presentations in geometry lessons

Introduction

Organizing a subject teacher’s media library
Using presentations to illustrate definitions
Using presentations to illustrate theorems
Using presentations to illustrate problems

Part II Digital Educational Resources

7th grade

Initial geometric information
Comparison of line segments and angles
Measuring segments. Blitz Poll
Beam, angle, adjacent and vertical angles.
Tests in Excel
Perpendicular lines
Adjacent and vertical corners
The first sign of equality of triangles
Medians, bisectors and heights of a triangle
Isosceles triangle. Properties of an isosceles triangle
Properties of an isosceles triangle. Problem solving
The second sign of equality of triangles
The third sign of equality of triangles
Median, bisector, height, triangles.
Tests in Excel
Circle and Circle
Construction tasks
Parallel lines.
Signs of parallel lines
Parallel lines. Converse theorems
Sum of triangle angles
Signs of equality of right triangles

8th grade

Polygons.
quadrilateral
Parallelogram. Parallelogram properties
Parallelogram. Signs of a parallelogram
Trapeze
Thales' theorem
Rectangle, rhombus, square
Rectangle area
Parallelogram area
Area of a triangle
Areas of figures
Trapezium area
Pythagorean theorem
Theorem converse to the Pythagorean theorem
Similar triangles. Proportional segments
The first sign of the similarity of triangles
Collection of problems. The first sign of the similarity of triangles
The second and third signs of the similarity of triangles
Middle line of the triangle
Proportional segments in a right triangle.
Practical applications of similar triangles
Sine, cosine and tangent of an acute angle of a right triangle
Tangent to a circle. Tangent property
Central and inscribed angles
Collection of problems. Central and inscribed angles
Four wonderful points of the triangle
Inscribed and Circumscribed Circles

Grade 9

Vector concept
Addition and subtraction of vectors
Multiply a vector by a number
Vector coordinates
The simplest problems in coordinates
Equation of a circle
Sine, cosine and tangent of angle
Triangle area theorem
Theorem of sines.
Cosine theorem
Dot product of vectors
Dot product of vectors in coordinates
Movements. Symmetry about a point
Movements. Symmetry about a straight line
Movements. Turn. Parallel transfer
Crafts on the theme “Movements”

Part 3 Methodological development of lessons

7th grade

Open day at the gymnasium. Triangles. Signs of equality of triangles
triangle inequality
Final test (Specification of experimental examination work in geometry for 7th grade students of Municipal Educational Institution Gymnasium No. 1)

8th grade

Master class “Using PowerPoint presentations in geometry lessons” [, 408.64 Kb] The master class was held as part of the international seminar “Organization of a developmental space in the context of integrated education for children: from the experience of the education department of the city of Polyarnye Zori in the implementation of an international project “ Border Gymnasium."

Grade 9

Vector addition
Coordinate method (Competition materials “Teacher’s Workshop”. The competitive development includes 4 lessons on the topic)
- Lesson 1. Vector coordinates
- Lesson 2. Coordinates of the sum and difference of vectors
- Lesson 3. The simplest problems in coordinates
- Lesson 4. Vector length.

To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com

Slides captions:

Similar triangles

Similar figures Figures are usually called similar if they have the same shape (similar in appearance).

Similarity in life (area maps)

Proportional segments Definition: segments are called proportional if their length is proportional. 12 6 8 4 A 1 B 1 AB C 1 K 1 SK They say that the segments A 1 B 1 and C 1 K 1 are proportional to the segments AB and SK. Are the segments AB and SC proportional to the segments EP and NT if: a) AB = 15 cm, SC = 2.5 cm, EP = 3 cm, NT = 0.5 cm? b) AB = 12 cm, SC = 2.5 cm, EP = 36 cm, NT = 5 cm? c) AB = 24 cm, SC = 2.5 cm, EP = 12 cm, NT = 5 cm? yes no no A B 6 cm C K 4 cm A 1 B 1 12 cm C 1 8 cm K 1

b Proportional segments Test 1. Indicate the correct statement: a) segments AB and RN are proportional to segments SC and ME; b) segments ME and AB are proportional to segments RN and SC; c) segments AB and ME are proportional to segments RN and SC. A B 3 cm C K 2 cm M E 9 cm RN 6 cm Appendix: the equality ME AB RN SK can be written by three more equalities: RN SK ME AB; ME RN AB SK; AB SK ME RN.

Proportional segments 2. Test F Y Z R L S N 1 c m 2 cm 4 cm 2 cm 3 cm Which segment must be entered to make the statement true: segments FY and YZ are proportional to segments LS and ……. a) RL; b) RS; c) SN a) RL

Proportional segments (necessary property) The bisector of a triangle divides the opposite side into segments proportional to the adjacent sides of the triangle. H Given: ABC, AK - bisector. Proof: 1 A B K C 2 Since AK is a bisector, then 1 = 2, which means that ABC and ASK have equal angles, therefore Prove: VK AB KS AC S ABC S ASK AB ∙ AK AC ∙ AK AB AC AVK and ASK have a common height AN, which means S AVK S ASK VK K C AB A C BK K S VC AB KS AC Therefore, Let's carry out AN BC.

Similar Triangles Definition: Triangles are called similar if the angles of one triangle are equal to the angles of another triangle and the sides of one triangle are proportional to the similar sides of the other. A 1 B 1 C 1 A B C Similar sides in similar triangles are the sides lying opposite equal angles. A 1 = A, B 1 = B, C 1 = C A 1 B 1 B 1 C 1 A 1 C 1 AB BC AC k A 1 B 1 C 1 ABC K – similarity coefficient ~

Similar triangles A 1 B 1 C 1 A B C Required property: A 1 = A, B 1 = B, C 1 = C, AB BC AC A 1 B 1 B 1 C 1 A 1 C 1 1 k ABC ~ A 1 B 1 C 1 , – similarity coefficient 1 k A 1 B 1 C 1 ABC , K – similarity coefficient ~

Solve problems 3. Using the data in the drawing, find the sides AB and B 1 C 1 of similar triangles ABC and A 1 B 1 C 1: A B C A 1 C 1 B 1 6 3 4 2.5? ? Find the sides A 1 B 1 C 1, similar to ABC, if AB = 6, BC = 12. AC = 9 and k = 3. 2. Find the sides A 1 B 1 C 1, similar to ABC, if AB = 6, BC = 12. AC = 9 and k = 1/3.

Theorem 1. The ratio of the perimeters of similar triangles is equal to the similarity coefficient. M K E A B C Given: MKE ~ ABC, K – similarity coefficient. Prove: P MKE: P ABC = k Proof: K , MK AB KE BC ME AC So, MK = k ∙ AB, KE = k ∙ BC, ME = k ∙ AC. Since according to the condition MKE ~ ABC, k is the similarity coefficient, then P MKE = MK + KE + ME = k ∙ AB + k ∙ BC + k ∙ AC = k ∙ (AB + BC + AC) = k ∙ P ABC. This means P MKE: P ABC = k.

Theorem 2. The ratio of the areas of similar triangles is equal to the square of the similarity coefficient a. M K E A B C Given: MKE ~ ABC, K – similarity coefficient. Prove: S MKE: S ABC = k 2 Proof: Since according to the condition MKE ~ ABC, k is the similarity coefficient, then M = A, k, MK AB ME AC means MK = k ∙ AB, ME = k ∙ AC. S MKE S ABC MK ∙ ME AB ∙ AC k ∙ AB ∙ k ∙ AC AB ∙ AC k 2

Solve the problems Two similar sides of similar triangles are 8 cm and 4 cm. The perimeter of the second triangle is 12 cm. What is the perimeter of the first triangle? 24 cm 2. Two similar sides of similar triangles are 9 cm and 3 cm. The area of the second triangle is 9 cm 2. What is the area of the first triangle? 81 cm 2 3. Two similar sides of similar triangles are 5 cm and 10 cm. The area of the second triangle is 32 cm 2. What is the area of the first triangle? 8 cm 2 4. The areas of two similar triangles are 12 cm 2 and 48 cm 2. One of the sides of the first triangle is 4 cm. What is the similar side of the second triangle? 8 cm

Solution to the problem The areas of two similar triangles are 50 dm 2 and 32 dm 2, the sum of their perimeters is 117 dm. Find the perimeter of each triangle. Find: R ABC, R REC Solution: Since by condition the triangles ABC and REC are similar, then: Given: ABC, R REC are similar, S ABC = 50 dm 2, S REC = 32 dm 2, R ABC + R REC = 117dm. S ABC S REC 50 32 25 16 K 2 . So, k = 5 4 K, R ABC R REC R ABC R REC 5 4 1.25 So, R ABC = 1.25 R REC Let R REC = x dm, then R ABC = 1.25 x dm T. to According to the condition R ABC + R REK = 117 dm, then 1.25 x + x = 117, x = 52. This means P REK = 52 dm, P ABC = 117 – 52 = 65 (dm). Answer: 65 dm, 52 dm.

“Mathematics should be taught only then because it puts the mind in order” M.V. Lomonosov I wish you success in your studies! Mikhailova L.P. GOU TsO No. 173.

Let us depict: a) two unequal circles; b) two unequal squares; c) two unequal isosceles right triangles; d) two unequal equilateral triangles. a) two unequal circles; b) two unequal squares; c) two unequal isosceles right triangles; d) two unequal equilateral triangles. How are the figures in each pair presented different? What do they have in common? Why are they not equal?

In similar triangles ABC and A 1 B 1 C 1 AB = 8 cm, BC = 10 cm, A 1 B 1 = 5.6 cm, A 1 C 1 = 10.5 cm. Find AC and B 1 C 1. A B C A1A1 B1B1 C1C,6 10.5 similar,6 10.5 x y Answer: AC = 14 m, B 1 C 1 = 7 m.

Physical education lesson: The lesson has been dragging on for a long time. You have decided a lot. The bell will not help here, Since your eyes are tired. We do everything at once. We repeat four times. – Follow the similarity sign with your eyes. - Close your eyes. – Relax your forehead muscles. – Slowly move your eyeballs to the far left position. – Feel the tension in your eye muscles. – Fix the position – Now slowly, with tension, move your eyes to the right. – Repeat four times. - Open your eyes. – Follow the similarity sign with your eyes.

The first sign of similarity Theorem. (The first sign of similarity.) If two angles of one triangle are equal to two angles of another triangle, then such triangles are similar. A B C C1C1 B1B1 A1A1 C"C" B"

Geometry

chapter 7

Prepared by Daria Kirillova, 9th grade student

Teacher Denisova T.A.

1.Definition of similar triangles

a) proportional segments

b) definition of similar triangles

c) Area ratio

a) The first sign of similarity

b) Second sign of similarity

c) The third sign of similarity

a) Midline of the triangle

b) Proportional segments in a right triangle

c) Practical applications of triangle similarity

b) The value of sine, cosine and tangent for angles 30 0, 45 0 and 60 0

The relationship between segments AB and CD is called the ratio of their lengths, i.e. AB:CD

AB = 8 cm

CD = 11.5 cm

Segments AB and CD are proportional to segments A 1 IN 1 and C 1 D 1 , If:

AB= 4 cm

CD= 8 cm

WITH 1 D 1 = 6 cm

A 1 IN 1 =3 cm

Similar figures- these are figures of the same shape

If in triangles all angles are respectively equal, then the sides lying opposite equal angles are called similar

Let in triangles ABC and A 1 IN 1 WITH 1 the angles are respectively equal

Then AB and A 1 IN 1 ,VS and V 1 WITH 1 ,SA and C 1 A 1 -similar

Two triangles are called similar , if their angles are respectively equal and the sides of one triangle are proportional to the similar sides of the other triangle

K- similarity coefficient

back

The sides of one triangle are 15 cm, 20 cm, and 30 cm. Find the sides of a triangle similar to this if the perimeter is 26 cm

The ratio of the areas of two similar triangles equal to the square of the similarity coefficient

Proof:

The similarity coefficient is equal to K

S and S 1 are the areas of triangles, then

According to the formula we have

The first sign of the similarity of triangles

If two angles of one triangle are respectively equal to two angles of another, then such triangles are similar

Prove:

Proof

1)By the theorem on the sum of the angles of a triangle

2) Let us prove that the sides of the triangles are proportional

Same with the corners

So the sides

proportional to similar sides

The second sign of similarity of triangles

If two sides of one triangle are proportional to two sides of another triangle and the angles between these sides are equal, then such triangles are similar

Prove:

Proof

The third sign of similarity of triangles

If three sides of one triangle are proportional to three sides of another, then such triangles are similar

Prove:

Proof

Middle line called a segment connecting the midpoints of its two sides

Theorem:

The midline of a triangle is parallel to one of its sides and equal to half of that side

Prove:

Proof

Theorem:

The medians of a triangle intersect at one point, which divides each median in a ratio of 2:1, counting from the vertex

Prove:

Proof

In triangle ABC, median AA 1 and BB 1 intersect at point O. Find the area of triangle ABC if the area of triangle ABO is equal to S

Theorem:

The altitude of a right triangle drawn from the vertex of a right angle divides the triangle into two similar right triangles, each of which is similar to the given triangle

Prove:

Proof

Theorem:

The height of a right triangle drawn from the vertex of a right angle is the average proportional to the segments into which the hypotenuse is divided by this height

Prove:

Proof

Determining the height of an object:

Determine the height of a telegraph pole

From the similarity of triangles it follows:

Practical applications of similar triangles

Determining the distance to an invalid point:

Sinus - ratio of the opposite leg to the hypotenuse in a right triangle

Cosine - ratio of adjacent leg to hypotenuse in a right triangle

Tangent- ratio of the opposite side to the adjacent side in a right triangle

0 , 45 0 , 60 0

The value of sine, cosine and tangent for angles of 30 0 , 45 0 , 60 0

Similarity

Slides: 9 Words: 230 Sounds: 0 Effects: 117

Similarity of triangles. Solving problems using ready-made drawings, grade 8. Mathematics teacher of the first quarter category RMOU Obskaya secondary school Vodyanova E.A. Problem 1. Prove: ?ХZR ~ ?RYZ Z Y 40° X 40° R. Problem 2. ABCD - trapezoid Prove: ?BOC ~ ?DOA B C O A D. Problem 3. ABCD - trapezoid Prove: ?ABC ~ ?ACD B C A D Name the proportional segments. Problem 4. BD || AF Find: AC; AB C 2 cm B D 3 cm A F 12 cm. Problem 5. KM || FH Find: FH H 4 cm K 7 cm 5 cm F M L. Problem 6. Find: AB C 2 cm 1 cm D B 5 cm 10 cm A F. Problem 7. Find: BD B 2 cm F D 5.5 cm 2 cm A C. Problem 8. ABCD - parallelogram Find: BD B C 16 cm 12 cm 8 cm D A R F. - Similarity.ppt

similarity of triangles

Slides: 12 Words: 480 Sounds: 0 Effects: 85

Similar triangles. Proportional segments. Definition of similar triangles. The number k, equal to the ratio of similar sides of the triangles, is called the similarity coefficient. The ratio of the areas of similar triangles. The ratio of the areas of two similar triangles is equal to the square of the similarity coefficient. The bisector of a triangle divides the opposite side into segments proportional to the adjacent sides of the triangle. Signs of similarity of triangles. III sign of similarity of triangles If three sides of one triangle are proportional to three sides of another triangle, then such triangles are similar Given: ?ABC, ?A1B1C1, Prove: ?ABC ?A1B1C1. - Similarity of triangles.ppt

Similar triangles

Slides: 19 Words: 322 Sounds: 0 Effects: 72

Geometry. Triangle. Let's remember. Similar figures. How are the figures similar? Form! Definition of similar triangles. Signs of similarity of triangles. The angles are respectively equal. C1. Similar sides. Proportional. Similarity coefficient “k”. Name the similarities. Equality of relations between similar parties. Which triangles are similar? Circles are always similar. Squares are always similar. Very interesting. Shadow from the pyramid. Shadow from a stick. A little more about triangles. Proportional segments in a triangle. The height of the triangle. The altitudes of the triangle intersect at one point O, called the orthocenter. - Similar triangles.ppt

Similarity of triangles grade 8

Slides: 6 Words: 164 Sounds: 0 Effects: 0

Application of similarity in human life. 1 sign of triangle similarity. 2 sign of similarity of a triangle. 3 sign of similarity of a triangle. Problem No. 1. Sides a and d, b and c are similar. Problem No. 2. - Similarity of triangles, grade 8.ppt

“Similar triangles” 8th grade

Slides: 42 Words: 1528 Sounds: 2 Effects: 381

Similar triangles. Table of contents. Proportional segments. Segments. In everyday life there are objects of the same shape. Definition of similar triangles. Task. Similar sides. Two triangles are called similar. Similarity of triangles. The ratio of the areas of similar triangles. Theorem. Properties of similarity. Triangles have equal angles. Signs of similarity of triangles. First sign. Similar sides are proportional. Second sign. General side. Third sign. The middle line of the triangle. Middle line. Medians in a triangle. O – intersection of medians. - “Similar triangles” 8th grade.ppt

Geometry Similarity of triangles

Slides: 9 Words: 405 Sounds: 0 Effects: 0

Educational theme of the project. Similar triangles. Signs of similarity of triangles. Creative theme of the project: Abstract. The project was prepared outside of school hours by 8th grade students. Implemented within the framework of 8th grade geometry on the topic “signs of similarity of triangles.” The project includes an information and research part. Analytical work with information systematizes knowledge about such figures. Didactic tasks will help monitor the degree of mastery of educational material. Reflection? Questions: What does the concept of “similar triangles” mean? How to measure the height of large buildings, trees...? - Geometry Similarity of triangles.ppt

Geometry "Similar Triangles"

Slides: 36 Words: 1995 Sounds: 0 Effects: 191

Similar triangles. Proportional segments. Property of the bisector of a triangle. Two triangles are called similar. Problem solving. Theorem on the ratio of areas of similar triangles. The first sign of similarity of triangles. The second sign of similarity of triangles. Sides of a triangle. The third sign of similarity of triangles. Mathematical dictation. Proportionality of the sides of an angle. Similarity of right triangles. Continuation of the sides. The middle line of the triangle. The two sides of the triangle are connected by a segment not parallel to the third. Proportional segments in a right triangle. - Geometry “Similar triangles”.ppt

Definition of similar triangles

Slides: 48 Words: 2059 Sounds: 0 Effects: 138

Similar triangles. Uses in life. Definition of similar triangles. Table of contents. Proportional segments. Two triangles are called similar. The ratio of the areas of similar triangles. The first sign of the similarity of triangles. The second sign of the similarity of triangles. The third sign of similarity of triangles. Triangle ABC. The sides of triangle ABC are proportional. The sides of triangle ABC are proportional to similar sides. Consider triangle ABC. ABC. Triangles ABC and ABC are equal on three sides. Practical applications of triangle similarity. - Definition of similar triangles.ppt

Signs of similarity

Slides: 24 Words: 618 Sounds: 0 Effects: 154

Similar triangles. Signs of similarity of triangles. Definition of similar triangles. The first sign of similarity of triangles. Given. Prove: Proof: So, the sides of triangle ABC are proportional to similar sides of triangle A1B1C1. The second sign of similarity of triangles. 13. 16. The third sign of similarity of triangles. Proof of the theorem. Theorem: Given: ?ABC, ?A1B1C1 AB/A1B1=BC/B1C1=CA/C1A1. Taking into account the second criterion for the similarity of triangles, it is enough to prove that Similarity criteria.ppt

Signs of similarity of triangles

Slides: 8 Words: 224 Sounds: 0 Effects: 100

Signs of similarity of triangles. 1. Sign of similarity of triangles at two angles. There are three signs of similarity: A in a1b1. 3. Sign of similarity of triangles on three sides. Similarity of right triangles. - Signs of similarity of triangles.ppt

Three signs of similarity of triangles

Slides: 75 Words: 2318 Sounds: 0 Effects: 117

Similarity in geometry. Theme: "Similarity". Proportional segments. Two right triangles. Proportionality of segments. Similar figures. Figures of the same shape are called similar figures. Similar triangles. Two triangles are called similar if their angles are respectively equal. Similarity coefficient. Additional properties. Perimeter ratio. Common multiplier. Area ratio. Property of the bisector of a triangle. Bisector. The equation. Signs of similarity of triangles. The first sign of similarity of triangles. The angles of the triangles are respectively equal. Similar sides are proportional. - Three signs of similarity of triangles.ppt

Lesson Signs of similarity of triangles

Slides: 11 Words: 161 Sounds: 0 Effects: 91

Geometry lesson “Signs of similarity of triangles.” Objective of the lesson: Generalization on the topic “Signs of similarity of triangles.” Lesson objectives: Similar figures. In similar figures the angles are equal. In such figures, the sides are proportional. Are the triangles similar? When. The first sign of similarity of triangles. If two sides of one triangle are proportional to two sides of another. Then such triangles are similar. The second sign of similarity of triangles. if the three sides of one triangle are proportional to the three sides of another, the third sign of similarity of triangles. - Lesson Signs of similarity of triangles.ppt

The first sign of the similarity of triangles

Slides: 15 Words: 583 Sounds: 0 Effects: 163

Blue light. Similarity of triangles. The first sign of similarity. Let's depict: What is the difference between the figures in each presented pair? Definition. The proportionality coefficient is called the similarity coefficient. What do you mean what? Is ABC similar to a triangle? A1B1C1? The angles are equal. The sides are proportional. Similarity, resemblance. Indicate the proportional sides. The sides of the triangle are 5 cm, 8 cm and 10 cm. In similar triangles ABC and A1B1C1 AB = 8 cm, BC = 10 cm, A1B1 = 5.6 cm, A1C1 = 10.5 cm. Physical education: Do it all at once Repeat four times . 2. Set aside: segment AB"= A1B1 (point B" є AB) straight line B"C" || Sun. - The first sign of similarity of triangles.ppt

Ratio of areas of similar triangles

Slides: 6 Words: 250 Sounds: 0 Effects: 35

Similar triangles. Content. Similar figures. In everyday life, there are objects of the same shape, but of different sizes. In geometry, figures of the same shape are called similar. The number k, equal to the ratio of similar sides of the triangles, is called the similarity coefficient. The ratio of the perimeters of similar triangles. The ratio of the perimeters of two similar triangles is equal to the similarity coefficient. The ratio of the areas of similar triangles. The ratio of the areas of two similar triangles is equal to the square of the similarity coefficient. - Ratio of areas of similar triangles.ppt

Application of similarity

Slides: 11 Words: 457 Sounds: 0 Effects: 9

Application of similarity to problem solving. 8th grade. Conversation. Option 1 Determine similar triangles. Formulate the third criterion for the similarity of triangles. State the bisector property of a triangle. Option 2 Determination of the midline of the triangle. Formulate the first sign of similarity of triangles. State the property of the intersection point of the medians of a triangle. Oral work. What fraction of the area of triangle ABC is the area of trapezoid AMNC? Problem solving. Calculate the medians of a triangle with sides 25 cm, 25 cm and 14 cm. O is the point of intersection of the diagonals of the parallelogram ABCD, E and F are the midpoints of the sides AB and BC, OE = 4 cm, OF = 5 cm. - Application of similarity.ppt

Application of triangle similarity

Slides: 8 Words: 127 Sounds: 0 Effects: 29

Practical application of triangle similarity. Lesson plan. Application of similarity of triangles in proving theorems. Construction tasks. Measurement work on the ground. Triangle midline theorem. Property of medians of a triangle. Proportional segments in a right triangle. Division of a segment in a given ratio. Construction of triangles. Divide the segment in a ratio of 2/3. Determining the height of an object. Determining the distance to an inaccessible point. Determining the height of an object using a mirror. - Application of similarity of triangles.ppt

Application of the similarity of triangles in life

Slides: 31 Words: 1146 Sounds: 0 Effects: 12

Practical application of triangle similarity. Similarity in life. A little bit of history. The rod is approximately the height of a person. Determining the height of an object. Determining the height of the pyramid. Historical reference. Tired stranger. Thales. Thales' method. Shadow from a stick. Determining the height of an object using a pole. Mysterious Island. Finding the fourth unknown term of the proportion. Determining the height of an object from a puddle. Determining the height of an object using a mirror. Advantages. Determining the distance to an inaccessible point. Finding the width of the lake. Distance to tree. Pin measuring device. - Application of the similarity of triangles in life.ppt

Practical application of triangle similarity

Slides: 16 Words: 530 Sounds: 0 Effects: 0

practical application of triangle similarity. Fairy tale. Shrek's birthday. Shrek came home. Geometry lessons. Similarity of triangles. Everything was decided correctly. The distance from one shore to the other. You can use the similarity of triangles. Solution. Rope of the required length. Idea. Bracelet. - Practical application of triangle similarity.pptx

Practical applications of similar triangles

Slides: 10 Words: 454 Sounds: 0 Effects: 0

Topic: Practical applications of triangle similarity. Creative name: Determining the height of an object. How can you measure the height of an object using simple devices? What methods are there to determine the height of an object? What instruments or devices are needed to measure the height of an object? What are the similarities and differences in determining the height of an object? Study topic question: Application of similarity of triangles. Academic subjects: geometry, literature, physics. Participants: 8th grade students. Presentation-abstract, booklet, newsletter on methods for determining the height of an object. - Practical applications of similarity of triangles.ppt

Problems like

Slides: 21 Words: 436 Sounds: 0 Effects: 1

Solving geometry problems using ready-made drawings. Task topics. The first sign of similarity of triangles. The second and third signs of similarity of triangles. Similar triangles. Example No. 2. Example No. 1. Example No. 4. Example No. 3. Example No. 6. Example No. 7. Example No. 5. - Similar problems.ppt

Problems similar to triangles

Slides: 38 Words: 1448 Sounds: 0 Effects: 48

Similarity of triangles. The first sign of similarity. What triangles are called similar. Formulate the first sign of similarity of triangles. The triangles shown in the figure. Draw a triangle. Triangle. Sides of a triangle. Right triangles. The two triangles are similar. Sides of triangles. Perimeter. List all similar triangles. Side. Square. Vertex. Is it possible to intersect a triangle with a straight line? Chords of a circle. Find similar triangles. Acute triangle. Product of segments. Radius of a circle. Circle. Two straight. - Problems similar to triangles.ppt

Similarity of triangles problem solving

Slides: 6 Words: 331 Sounds: 0 Effects: 0

Similar triangles. The concept of similarity is one of the most important in the planimetry course. The study of the topic begins with the formation of the concepts of the relationship of segments and the similarity of triangles. Solving construction problems using the similarity method is discussed with students interested in mathematics. This topic is intended for 8th grade students. 19 hours are allocated for studying the material. Lesson topic: The first sign of similarity of triangles. Checking homework. Solving problems to prepare students to perceive new material. Learning new material. Formulation of 1 criterion for the similarity of triangles. Proof of the theorem. - Similarity of triangles problem solving.ppt

Triangle similarity problems

Slides: 22 Words: 326 Sounds: 0 Effects: 48

Similarity of triangles. Lesson motto. Individual card. Name similar triangles. Solving practical problems. Determining the height of the pyramid. Thales' method. Shadow from a stick. Measuring the height of large objects. Determining the height of an object. Determining the height of an object using a mirror. Determining the height of an object from a puddle. Solving problems using ready-made drawings. Gymnastics for the eyes. Independent work. -