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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

A B C D

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

Ex 1: Proof w/ overlapping triangles C 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

Ex 2: Proof w/ overlapping triangles Q 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

Proofs w/ overlapping triangles M 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

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)

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

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