7.3 Proving Triangles Similar using AA, SSS, SAS.

Slides:

Advertisements

Similar presentations

Concept: Use Similar Polygons

Advertisements

Section 9-3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

8.5 Proving Triangles Similar

Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

7-3: Identifying Similar Triangles

Lesson 7-1: Using Proportions

Honors Geometry Section 8.3 Similarity Postulates and Theorems.

GOAL 1 USING SIMILARITY THEOREMS 8.5 Proving Triangles are Similar THEOREMS Side-Side-Side Similarity Theorem Side-Angle-Side Similarity Theorem.

Lesson 5-4: Proportional Parts

7-3 Proving Triangles Similar. Triangle Similarity Angle-Angle Similarity Postulate: If two angles of one triangle are congruent to two angles of another.

7-3 Proving Triangles Similar

LESSON 8.3: Similar Polygons

10.2 Proving Triangles Similar Geometry Mr. Calise.

Benchmark 37 I can identify two triangles as similar using SSS, SAS, or AA triangle proportionality theorem.

3.4: Using Similar Triangles

Chapter 7.1 Common Core G.SRT.5 - Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Objective –

Using Proportions to Solve Geometry Problems Section 6.3.

Assignment P : 1-4, 7, 8, 10, 12, 14-17, 20, 30, 31, 32, 36, 41, 42 P : 4, 6-8, 10-14, 33, 39, 40 Challenge Problems.

Sections 8-3/8-5: April 24, Warm-up: (10 mins) Practice Book: Practice 8-2 # 1 – 23 (odd)

8-3 Proving Triangles Similar Learning Target: I will be able to prove triangles are similar. Goal 2.03.

Chapter 7 Similarity. Definition: Ratio The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle 4x+2x+5x+5x+2x = x.

Dilations and Scale Factors

Chapter 7: Proportions and Similarity

U SING S IMILARITY T HEOREMS THEOREM S THEOREM 8.2 Side-Side-Side (SSS) Similarity Theorem If the corresponding sides of two triangles are proportional,

6.5 – Prove Triangles Similar by SSS and SAS Geometry Ms. Rinaldi.

“Why so serious?”.

Special Topics Eleanor Roosevelt High School Chin-Sung Lin.

Similarity in Triangles Unit 13 Notes Definition of Similarity.

1 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt Ratios/ Proportions Similar.

Similarity Tests for Triangles Angle Angle Similarity Postulate ( AA~) X Y Z RT S Therefore,  XYZ ~  RST by AA~

Warm-Up Since they are polygons, what two things must be true about triangles if they are similar?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm up 1.What is the ratio of the corresponding side lengths for two congruent triangles?

(AA, SSS, SAS). AA Similarity (Angle-Angle) If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.

Geometry Sections 6.4 and 6.5 Prove Triangles Similar by AA Prove Triangles Similar by SSS and SAS.

Warm-Up: Review from ) Determine whether the two triangles are similar. If so, write the similarity statement and scale factor. If not, explain your.

8-3 Proving Triangles Similar M11.C B

Chapter 7 Quiz Review Lessons

Lesson 5-4: Proportional Parts 1 Proportional Parts Lesson 5-4.

Introduction Archaeologists, among others, rely on the Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity statements to determine.

Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.

Question about homework? Any questions on the homework? (choose random problems)

Section 7-4 Similar Triangles.

Chapter 8 Similarity Section 8.5 Proving Triangles are Similar U SING S IMILARITY T HEOREMS U SING S IMILAR T RIANGLES IN R EAL L IFE.

Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. AB C.

Congruence, Constructions and Similarity

U W VX Z Y XYZ 5/ Warm Up.

The product of the means equals the product of the extremes.

 There are 3 ways to show two triangles are similar to each other. Those 3 ways are: 1. Angle-Angle Similarity Postulate. (AA~) 2. Side-Angle-Side Similarity.

Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

7.3 Proving Triangles Similar

Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find.

Section Review Triangle Similarity. Similar Triangles Triangles are similar if (1) their corresponding (matching) angles are congruent (equal)

CONGRUENT TRIANGLES Side-Side-Side Postulate (SSS) Side-Side-Side Congruence: If the sides of one triangle are congruent to the sides of a second triangle,

Homework Questions: If you have questions on any of the following homework assignments, please write the problem number on the board. 7.1 worksheet 7.2.

Similarity Chapter Ratio and Proportion  A Ratio is a comparison of two numbers. o Written in 3 ways oA to B oA / B oA : B  A Proportion is an.

Similarity Tests for Triangles Angle Angle Similarity Postulate ( AA~) X Y Z RT S Therefore,  XYZ ~  RST by AA~

Proving Side-Side-Side. Proving Side-Angle-Side Create a 55 ° angle. Its two sides should be 3.5 and 5 inches long. Enclose your angle to make a triangle.

6.5 Prove Triangles Similar by SSS and SAS

Goal Identify and use similar triangles.

7-5: Parts of Similar Triangles

Lesson 5-4: Proportional Parts

5.2 Similar Polygons Two congruent polygons are also similar polygons.

Lesson 5-4 Proportional Parts.

7.1 Ratio and Proportions.

7-3 Triangle Similarity: AA, SSS, SAS

Similarity Tests for Triangles

Use Similar Polygons & AA Postulate

8.5 Proving Triangles are Similar

8-5 Proving Triangles Similar

Lesson 7-4 Proportional Parts.

Presentation transcript:

7.3 Proving Triangles Similar using AA, SSS, SAS. Course: Geometry pre-IB Quarter: 2nd Objective: Identify and use similar triangles. SSS: MA.B.1.4.3, MA.C.2.4.1, MA.C.3.4.1

W is reflexive and both triangles have a right  . Angle-Angle (AA) ~ Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. W X V Y Z W is reflexive and both triangles have a right  . ΔWVX ~ ΔWZY by AA ~ Post.

In the diagram, ΔWZY ~ ΔWVX by AA ~ Postulate Find x. Set up a proportion. Cross multiply. Distribute and foil. 16x + 8 = x2 + 10x + 16 0 = x2 - 6x + 8 x = 2 or 4 W 8 X V x+2 x Z 2x+1 Y

Finding Distances Indirectly You are at an indoor climbing wall. Using a mirror to see the top of the wall: CE = 85 ft. AC = 6.5 ft. AB = 5 ft. How tall is the wall? The triangles are similar by AA ~ Postulate. 1. Write proportion 2. Substitute given values 3. Solve for DE D B C A E

Side-Side-Side (SSS) ~ Theorem If the lengths of the 3 corresponding sides of two triangles are proportional, then the triangles are similar. Side-Angle-Side (SAS) ~Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the 2 pairs of sides including these angles are proportional, then the triangles are similar.

AC = 6, AD = 10, BC = 9, BE = 15. Describe how to prove that ΔACB ~ ΔDCE. CD = ? EC= ? Show that corresponding sides are proportional. Then use SAS Similarity with vertical angles ACB and DCE.

Using the SSS Similarity Theorem Which of these three triangles are similar? 1. Compare ratios of side lengths of ΔABC and ΔDEF shortest sides longest sides remaining sides Because the ratios are all equal, ΔABC ~ ΔDEF. 2. Compare ratios of side lengths of ΔABC and ΔGHJ Because the ratios are not equal, ΔABC and ΔGHJ are not similar. Since ΔABC ~ ΔDEF and ΔABC is not ~ ΔGHJ, ΔDEF is not ~ ΔGHJ.

More About Scale Factors If corresponding sides of similar polygons are in the ratio a:b, then the ratio of the perimeters is a:b. the ratio of ANY two corresponding lengths is a:b (altitudes, medians, angle bisector segments, diagonals, etc.) The ratio of the areas is a2:b2

Use the given lengths to find the width LM of the river below. Write proportion and solve: 42 ft P L M 5 ft Q N 8 ft