Theorems for Similar Triangles

1
Theorems for Similar Triangles

• Lesson 7.5
• Pre-AP Geometry

2
Lesson Focus

• Two theorems for showing that two triangles are
  similar are presented in this lesson.
• These theorems, along with the definition of
  similarity and the AA Similarity Postulate,
  provide four ways to prove that two triangles are
  similar.

3
SAS Similarity Theorem

• If an angle of one triangle is congruent to an
  angle of another triangle and the sides including
  those angles are in proportion, then the
  triangles are similar.
• Triangle ABC is similar to triangle DEF because
  ?A and ?D are congruent and ABDE ACDF.

4
SSS Similarity Theorem

• If the sides of two triangles are in proportion,
  then the triangles are similar.
• ABDE ACDF BCEF
• The two triangles are similar

5
SAS/SSS Similarity Theorems

• Example 1 The measures of the sides of ?ABC are
  4, 5, and 7 and the measures of the sides of ?XYZ
  are 16, 20, and 28. Are the triangles similar?
• Example 2 In ?ABC, AB 2, AC 5, and BC 6.
  In ?XYZ, XY 2.5, YZ 2, and XZ 3. Is ?ABC
  ??XYZ?

6
SAS/SSS Similarity Theorems

• Example 3 Name similar triangles and give the
  postulate or theorem that justifies your answer.

7
SAS/SSS Similarity Theorems

• Example 4 Name similar triangles and give the
  postulate or theorem that justifies your answer.

8
SAS/SSS Similarity Theorems

• Example 5 Name similar triangles and give the
  postulate or theorem that justifies your answer.

9
SAS/SSS Similarity Theorems

• Example 6 If ?ABC ? ?DEF, does
  correspond to ?
• Does correspond to
  ?
• Does correspond to
  ?

10
SAS/SSS Similarity Theorems

• Example 7 Given ?B ? ?DEC
• Prove ?ABC ? ?DEC
• Proof
• Statements Reasons

11
Similar Triangles

• Remember, you must match corresponding vertices
  when naming similar triangles.

12
Similar Triangles

• Ways to prove triangles similar
• Definition of Similarity
• AA Similarity Postulate
• SAS Similarity Theorem
• SSS Similarity Theorem

13
Written Exercises

• Problem Set 7.5, p.266 2 - 12 (even) Handout
  7-5