DRILL Prove each pair of triangles are congruent. Given: PQ is congruent to QR and PS is congruent to SR. Given: AB ║ CD, BC ║ DA

Objectives: Use congruent triangles to plan and write proofs. Use congruent triangles to prove constructions are valid.

8.4 Using Triangle Congruence CPCTC

Corresponding parts When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are congruent, that means that ALL the corresponding parts are congruent. A C B That means that EG CB G E F What is AC congruent to? Segment FE

Corresponding parts of congruent triangles are congruent.

CPCTC Corresponding Parts of Congruent Triangles are Congruent. You can only use CPCTC in a proof AFTER you have proved congruence.

Ex. Proof Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.

Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR. Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given

Reasons: Statements: Given Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Reasons: Given Definition of a midpoint Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR

Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR. Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem

Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR. Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem SAS Congruence Postulate

Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR. Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem SAS Congruence Postulate CPCTC

Ex. 2: Using more than one pair of triangles. Given: 1≅2, 3≅4. Prove ∆BCE≅∆DCE Prove: segment DC is congruent to segment CD 2 4 3 1

Given: QSRP, segment PT≅ segment RT Prove: segment PS≅ segment RS 4 3 1 Statements: QS  RP PT ≅ RT Reasons: Given

Homework Page 429 #’s 1 – 10 and #12