Corresponding Parts in Congruent Triangles

Corresponding sides and angles Corresponding AnglesCorresponding sides AB C R S T AB RS BC ST AC RT

if two polygons are congruent, then their corresponding parts are congruent. For triangles, Corresponding parts of congruent triangles are congruent, or CPCTC. CP CTC

Ex. 1: Planning & Writing a Proof Given: AB ║ CD, BC ║ DA Prove: AB ≅CD Plan for proof: Show that ∆ABD ≅ ∆CDB. Then use the fact that corresponding parts of congruent triangles are congruent.

Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║ TR. Statements: 1.A is the midpoint of MT, A is the midpoint of SR. 2.MA ≅ TA, SA ≅ RA 3.  MAS ≅  TAR 4.∆MAS ≅ ∆TAR 5.  M ≅  T 6.MS ║ TR Reasons: 1.Given

Given:  1 ≅  2,  3 ≅  4. Prove ∆BCE ≅ ∆DCE Statements: 1.  1≅  2,  3≅  4 2.AC ≅ AC 3.∆ABC ≅ ∆ADC 4.BC ≅ DC 5.CE ≅ CE 6.∆BCE≅∆DCE Reasons: 1.Given