SSS Congruence Theorem

The page details the Side-Side-Side (SSS) congruence theorem with practical examples and proofs.

Definition: The SSS congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: A detailed proof showing ΔPQR ≅ ΔSTR where:

• PQ = ST
• QR = TR
• R is the midpoint of PS

Highlight: The proof plan must identify all three pairs of congruent sides before concluding triangle congruence.

SAS Congruence Theorem

This section covers the Side-Angle-Side (SAS) congruence theorem with detailed examples and applications.

Definition: The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Example: A proof demonstrating ΔJMN ≅ ΔLNM where:

• JM = LN
• ∠JMN = ∠LNM
• MN is common to both triangles

Advanced SAS Applications

The final page presents advanced applications of the SAS congruence theorem with complex examples.

Example: A proof showing ΔABD ≅ ΔCBD using:

• AB = CB
• BD bisects ∠ABC
• BD is common to both triangles

Highlight: The importance of identifying the included angle between congruent sides is emphasized throughout the proofs.

Vocabulary: Angle bisector creates two congruent angles, which is crucial for many SAS proofs.

Introduction to Triangle Congruence Proofs

This page introduces the five fundamental ways to prove triangles are congruent. The methods covered include SSS, SAS, ASA, AAS, and HL (Hypotenuse-Leg) theorems.

Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that when two triangles are proven congruent, their corresponding parts are also congruent.

Highlight: AAA (three pairs of congruent angles) does NOT prove triangle congruence.

Vocabulary: Included angle refers to the angle formed between two sides of a triangle.