University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

447

Pages:

2
Author:

Amelie Villegas

Proving Triangle Congruence by SAS Theorem 5.5 Side-Angle-Side (SAS) Congruence Theorem If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If AB ≅ DE, ∠A ≅ ∠D, and AC ≅ DF, then ΔABC ≅ ΔDEF Diagram: Shows two triangles, ΔABC and ΔDEF. Corresponding sides and angles are marked with congruent symbols (≅). Extra Practice Exercise 1: Given: BD ⊥ AC, AD ≅ CD Prove: ΔABD ≅ ΔCBD Two sets of proofs are shown: Statements: BD ⊥ AC ∠BDA = 90° ∠BDC = 90° ∠BDA ≅ ∠BDC AD ≅ CD BD ≅ BD ΔABD ≅ ΔCBD Reasons: Given Definition of ⊥ lines Definition of ⊥ lines Substitution (or Transitive) Given Reflexive By SAS Alternative Statements: BD ≅ BD BD ⊥ AC ∠BDA = 90° ∠BDC = 90° ∠BDA ≅ ∠BDC AD ≅ CD ΔABD ≅ ΔCBD Alternative Reasons: Reflexive Given Definition of ⊥ lines Definition of ⊥ lines Substitution Given By SAS 5.3 Problem 2 Given: JN = MN, NK = NL Prove: ΔJNK ≅ ΔMNL Statements: JN ≅ MN NK ≅ NL ∠JNK ≅ ∠MNL ΔJNK ≅ ΔMNL Reasons: Given Given Vertical angles by SAS Problem 3 In the diagram, P is the center of the circle. ∠EPF ≅ ∠GPH Explain your reasoning: PH ≅ PG ≅ PE ≅ PF Since all radii in a circle are the same. ΔEPF ≅ ΔHPG by SAS Problem 4 ABCDEF is a regular hexagon. Explain your reasoning: This means all sides and angles are equal. ΔABC ≅ ΔBCD by SAS Problem 5 A quilt is made of triangles. You know PS || QR and PS ≅ QR. Show that ΔPQR ≅ ΔRSP Statements: PS || QR ∠SPR ≅ ∠PRQ PS ≅ QR PR ≅ RP ΔPQR ≅ ΔRSP Reasons: Given Alternate Interior Angles Given Reflexive by SAS