Download Geometry Lesson 8-5 Similarity Proofs

Geometry Lesson 8-5 Similarity Proofs
Examples of Similarity Proofs
#1: Given: AB DE
Prove: BAC ~ EDC
Statements
Reasons
1)
1) given
2) B  E and A  D 2) If 2 parallel lines are cut by
transversal, then alternate interior
angles are congruent.
3) BAC ~ EDC
3) AA Similarity Theorem
OR use vertical angles
#2:
Statements
Reasons
1)
1) Given
2) CA=CD+DA
CB= CE+BE
2) Addition
3)
CA 9
CB 6
 and

CD 3
CE 2
CA CB
4) CD  CE
5) C  C
6) CDE ~ CAB
3) Substitution
4) Transitive or Substitution
5) reflexive property
6) SAS Similarity theorem
#3:
Statements
Reasons
1)
1) given
2)
2) given
3) TRV  SRV
3) Def. of angle bisector
4) TVW  W
4 Isosceles triangle theorem
5) TVW  SVR
5) Vertical angles are congruent
6) W  SVR
6) Substitution
7) TRW ~ SRV
7) AA Similarity Theorem
RW RV
8) TW  SV
8) Corresponding sides of similar
triangles are in proportion.
9) RW  SV  RV  TW
9) In a proportion, the product of the
means equals the product of extremes!