3. K

4. Aim: Do Now: How do we prove overlapping triangles are congruent?
State the names of two triangles in each diagram: 2) F M B R H 1) A B C D 3) S Q G L 4) A G K P D V

5. A B C D

6. Proofs w/overlapping triangles:
1) Re-draw the diagram, separating the triangles.
2) Use Reflexive Postulate if any shared sides or angles are needed in the proof. A B C D
Given:
Prove: A B C D
Given
Reflexive Postulate
S.S.S. Postulate
Geometry Lesson: Proofs With Overlapping Triangles

7. Ex 1: Proof w/ overlapping trianglesC
Given:
Prove:
Statements
Reasons 1) 2) 3) 4) 5) 6) 7)
Given
Given
Reflexive Postulate
Addition Postulate
Partition Postulate
Substitution Post.
S.A.S. Postulate
Geometry Lesson: Proofs With Overlapping Triangles

8. Ex 2: Proof w/ overlapping trianglesQ T S V N
Ex 2: Proof w/ overlapping triangles
Given:
Prove:
Statements
Reasons 1) 2) 3) 4) 5) 6) 7) 8)
Given
Def. Median
Def. Midpoint
Mult. Postulate
Substitution Post.
Reflexive Post.
S.A.S. Postulate
Geometry Lesson: Proofs With Overlapping Triangles
C.P.C.T.C

12. Proofs w/ overlapping trianglesM S T D E 1 2 3 4
Proofs w/ overlapping triangles
1) Given:
Prove: F L S R P
2) Given:
Prove: F M B R H
3) Given:
Prove:
Geometry Lesson: Proofs With Overlapping Triangles

13. Statements Reasons 1) 2) 3) 4) 5) 6) 7) 8) R M S T D E 1 2 3 4
1) Given:
Prove:
Statements
Reasons 1) 2) 3) 4) 5) 6) 7) 8)

14. F L S R P
2) Given:
Prove:
Statements
Reasons 1) 2) 3) 4) 5) 6) 7) 8)

15. 3) Given:
Prove: F M B R H
Statements
Reasons 1) 2) 3) 4) 5) 6) 7) 8)