5.2 Proving Triangles are Congruent: SSS and SAS

WARM UP ∆QRS ≅ ∆LMN. Name all pairs of congruent corresponding parts. Name the three sides of ∆ABC. QR  LM, RS  MN, QS  LN, Q  L, R  M, S  N

Objective SWBAT show triangles are congruent using SSS and SAS.

Side-Side-Side Congruence Postulate

Use the SSS Congruence Postulate From the diagram you know that HJ ≅ LJ and HK ≅LK. By the Reflexive Property, you know that JK ≅ JK Yes, there is enough information given. You can use the SSS Congruence postulate to conclude that ∆HJK ≅ ∆LJK

Side-Angle-Side Congruence Postulate

Use the SAS Congruence Postulate 𝑮𝑯 ≅ 𝑮𝑭 𝑮𝑬 ≅ 𝑮𝑬 <GEH ≅ <GEF 𝑨𝑩 ≅ 𝑩𝑪 <ABD ≅ <CBD 𝑫𝑩 ≅ 𝑫𝑩 You cannot conclude that ∆GHE ≅ ∆GFE because the congruent angles are not between the congruent sides. Using SAS you can conclude that ∆ABD ≅ ∆CBD

You Try State if the two triangles are congruent. If they are, state how you know. 1) 2) 3) Yes by SSS Yes by SAS Not Congruent

You Try State if the two triangles are congruent. If they are, state how you know. 4) 5) 6) Not Congruent Yes by SSS Yes by SAS

A proof is a convincing argument that shows why a statement is true A proof is a convincing argument that shows why a statement is true. A two-column proof has numbered statements and reasons that show the logical order of the argument. Each statement has a reason listed to its right.

3. Vertical Angle Theorem STATEMENTS Reasons 1. Given 2. Given 3. Vertical Angle Theorem 4. Definition of Midpoint 5. SAS Congruence Postulate

Reflexive Property of Congruence SSS Congruence Postulate Write a Proof Given Reflexive Property of Congruence SSS Congruence Postulate

Vertical Angles Theorem SAS Congruence Postulate You Try Given AC ≅ DC Vertical Angles Theorem SAS Congruence Postulate