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4-4 Proving Congruence- SSS, SAS

4-4 Proving Congruence- SSS, SAS. Congruent. Means that corresponding parts are congruent, Matching sides and angles will be congruent. B. A. C. Y. X. Z. Naming. ORDER MATTERS!!!!. Example 1. If two triangles are congruent… Name all congruent angles Name all congruent sides. R.

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4-4 Proving Congruence- SSS, SAS

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  1. 4-4 Proving Congruence- SSS, SAS

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

  3. B A C Y X Z

  4. Naming • ORDER MATTERS!!!!

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

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

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

  8. 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 X Y B A Z C

  9. Included angles

  10. 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. B D E F C A

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

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

  13. 4-5 Proving CongruenceASA and AAS

  14. 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.

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

  16. Angle-Angle-Side Congruence(AAS) • If 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.

  17. Given: <NKL <NJM and Prove: K J M L N Statement Reason Given 1. <NKL <NJM 1. ____________ 2. <N <N Reflexive 2.____________ KL = MN 3._____________ 3. Given 4. AAS 4. 5. CPCTC 5.___________

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