Goal Identify and use similar triangles.

Slides:

Advertisements

Similar presentations

Objectives Prove that two triangles are similar using AA, SAS, and SSS.

Advertisements

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

7-3 Proving Triangles Similar

Using Proportions to Solve Geometry Problems Section 6.3.

7.3 Proving Triangles Similar using AA, SSS, SAS.

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

Similarity in Triangles Unit 13 Notes Definition of Similarity.

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

Angle angle similarity. 47° 58° 75° 58° 75° Are the following triangles similar? E D F B A C

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?

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

Geometry 6.5 SWLT: Use the SSS & SAS Similarity Theorems.

8-3 Proving Triangles Similar M11.C B

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

Drill Write your homework in your planner Take out your homework Find all angle measures:

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

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.

4.5 – Prove Triangles Congruent by ASA and AAS In a polygon, the side connecting the vertices of two angles is the included side. Given two angle measures.

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)

Geometry-Part 7.

8.3 Methods of Proving Triangles Similar

7.4 Showing Triangles are Similar: SSS and SAS

Determine whether the two triangles are similar.

Proving Triangles Similar

Proving Triangles are Similar

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

Similarity Postulates

Take a warm-up from the ChromeBook, calculator, and compass

6.5 Prove Triangles Similar by SSS and SAS

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Objective: To use AA, SAS and SSS similarity statements.

Proving Triangles Congruent: SSS and SAS

Are there shortcut postulates or theorems for similarity?

Three ways to prove triangles congruent.

5.2 Similar Polygons Two congruent polygons are also similar polygons.

4-4 and 4-5: Congruent Triangle Theorems

5.3 Proving Triangle Similar

Z Warm Up W U 5 V X Y 6 XYZ 5/

Proving Triangles Similar

Proving Triangles Similar

7-3 Similar Triangles.

4-2 Some Ways to Prove Triangles Congruent (p. 122)

LT 7.4 Prove triangles are similar

Test study Guide/Breakdown

Proving Triangles Similar Related Topic

Proving Triangles Congruent

Similarity Tests for Triangles

CHAPTER 7 SIMILAR POLYGONS.

8.5 Proving Triangles are Similar

5.3 Proving Triangle Similar

Z Warm Up W U 5 V X Y 6 XYZ 5/

~ ≅ SIMILAR TRIANGLES SIMILAR SAME SHAPE, BUT NOT SAME SIZE CONGRUENT

Proving Triangles Congruent

Proving Triangles Similar.

8.3 Methods of Proving Triangles Similar

Section 8.5 Proving Triangles are Similar

6.5 – Prove Triangles Similar by SSS and SAS

6.5 – Prove Triangles Similar by SSS and SAS

Similar Triangles Panašūs trikampiai.

Proving Triangles Similar.

Proving Triangles Congruent

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

6-3/6-4: Proving Triangles Similar

Proving Triangles Congruent

Z Warm Up W U 5 V X Y 6 XYZ 5/

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

Goal Identify and use similar triangles

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

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 the lengths of 2 corresponding sides are proportional and the included angles are congruent , then the triangles are similar.

Prove the triangles are similar.

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.

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.