Proving Triangles Similar

Slides:

Advertisements

Similar presentations

Concept: Use Similar Polygons

Advertisements

I can identify corresponding angles and corresponding sides in triangles and prove that triangles are congruent based on CPCTC.

7-3 Proving Triangles Similar

Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.

Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

(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.

4-2 Triangle Congruence by SSS and SAS. Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another.

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

Triangle Similarity: Angle Angle. Recall Recall the definitions of the following: Similar Congruent Also recall the properties of similarity we discussed.

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. Congruence We know… Two SEGMENTS are congruent if they’re the same length. Two ANGLES are congruent if they have the same measure.

Geometry-Part 7.

4-2 Triangle Congruence by SSS and SAS

Proving Triangles are Congruent

8.3 Methods of Proving Triangles Similar

7.4 Showing Triangles are Similar: SSS and SAS

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

Similarity in Triangles

Please get a whiteboard, marker and eraser.

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?

Featuring ASA and AAS (angle-side-angle and angle-angle-side)

Inequalities in two triangles

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Proving Triangles Similar Same idea as polygons

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Three ways to prove triangles congruent.

4-2 Triangle Congruence by SSS and SAS

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 Same idea as polygons

7-3 Similar Triangles.

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

Applying Similarity Using the Angle-Angle (AA) Criterion (5.3.2)

ABC DEF? Is Do Now: When two triangles are congruent:

Proving Triangles Similar Related Topic

Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.

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 Similar.

8.3 Methods of Proving Triangles Similar

Agenda Investigation 8-3 Proving Triangles are Similar Class Work

SSS, SAS, ASA, & AAS Students will prove two triangles are congruent using the SSS, SAS, ASA, & AAS Postulates.

Proving Triangles Congruent

Similar Triangles Panašūs trikampiai.

Lesson Similarity of Triangles

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

Proving Triangles Similar.

Warmup Write a congruence statement for the triangles.

Objective We will analyze congruent triangles

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

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

How can you show that two triangles

Warm Up 1 ( Write a congruence statement

4-4/4-5 Proving Triangles Congruent

Proving Triangles Congruent

SSS SAS AA How do you use corresponding sides and angles to determine the similarity of triangles?

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

4-2 Triangle congruence by sss & sas

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

Proving Triangles Similar 10/22/12 Unit 2 Triangles Proving Triangles Similar (AA, SSS, SAS)

AA Similarity (Angle-Angle) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar….or the third pair of angles are congruent. Given: and Conclusion:

SSS Similarity (Side-Side-Side) If the measures of the corresponding sides of two triangles are in the same ratio, then the triangles are similar. 5 11 22 8 16 10 Given: Conclusion:

SAS Similarity (Side-Angle-Side) If the measures of two sides of a triangle are in the same ratio to the measures of two corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar. 5 11 22 10 Given: Conclusion: