4.2: Congruent Triangles  Two figures are congruent if they are the same ______ and same _______. sizeshape  Segments are congruent if they have the same length.  Angles are congruent if they have the same measure.

Congruent Triangles  Two triangles are congruent if each part of one triangle is congruent to a corresponding part of the other (both angles and sides… 6 altogether).

Congruent Triangles  We want to prove that two triangles are congruent. Luckily, we don’t have to go through and prove that every set of corresponding parts are congruent… we have some shortcuts… yippee!

Proving Triangles are Congruent  SSS postulate (side-side-side): (by SSS)  If 3 sides of one triangle are congruent to 3 sides of another, then the triangles are congruent.

Ex. 1  Given:  Prove:

Ex. 1  StatementReason 1) JK = JM, KL = MK1) Given 2)2) Reflexive Property 3) 3) SSS JL = JL

Proving Triangles are Congruent  SAS postulate (side-angle-side):  If 2 sides and the included angle of both triangles are congruent, then the triangles are congruent. (by SAS)

Proving Triangles are Congruent  ASA postulate (angle-side-angle):  If 2 angles and the included side of both triangles are congruent, then the triangles are congruent. (by ASA)

Ex. 2:  Given:  Prove:

Ex. 2  StatementReason 1) JK = ML, JK || ML1) Given 2)2) Reflexive Property 4) 4) SAS JL = JL 3) 3) Alternate Interior Angles Theorem

Ex. 3:  Given:  Prove:

Ex. 3  StatementReason 1) VW = ZY,1) Given 5) 5) ASA 3) 2) Definition of Perpendicular lines2) 3) Definition of Right Angle 4) 4) Transitive Property of Equality