4-4 Proving Congruence- SSS, SAS. Congruent Means that corresponding parts are congruent, Matching sides and angles will be congruent.

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Presentation transcript:

4-4 Proving Congruence- SSS, SAS

Congruent Means that corresponding parts are congruent, Matching sides and angles will be congruent

A B C Z Y X

Naming ORDER MATTERS!!!!

Example 1 If two triangles are congruent… –Name all congruent angles –Name all congruent sides S R T Y X Z

Reminder… If two angles of one triangle are congruent to two angles of another triangle then the 3 rd angles are congruent

Keep in mind You can flip, turn or slide congruent triangles and they will maintain congruency!!

Side-Side-Side Congruence (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent A B C X Y Z

Included angles

Side-Angle-Side Congruence (SAS) If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent. A B C D E F

Given that RQ||TS and RQ TS, Prove RQ||TS Given Alt. int. <‘s are congruent Reflexive SAS Q RS T

Given: Triangle CDE is an isosceles triangle. G is the midpoint of CE. Prove: C G E D Statement Reason 1.Given 2.Def. of Isosceles Triangle 3.Midpoint theorem 4.Reflexive property 5.SSS Triangle CDE is isosceles CD = ED CG = GE DG = DG

4-5 Proving Congruence ASA and AAS

Angle-Side-Angle Congruence (ASA) If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

Given: L is the midpoint of WE and WR||ED Prove: W R L D E <W <E because_________________ angles are ____________. By the___________________, WL___EL. Since vertical angles are _____________, ______________ and by ______ Alternate interior Congruent Def. of midpoint thrm = Congruent <RLW = <ELDASA

Angle-Angle-Side Congruence (AAS) non-includedIf 2 angles and a non-included side of one triangle are congruent to the corresponding 2 angles and side of another triangle, then the 2 triangles are congruent.

Given: <NKL <NJM and Prove: J L N M K StatementReason 1. <NKL <NJM1. ____________ 2. <N <N 2.____________ 3._____________3. Given AAS 5.___________ 5. CPCTC Given Reflexive KL = MN