Page 2: Practical Proofs Application

This page demonstrates practical applications of triangle congruence proofs using SSS and SAS postulates. Two detailed examples are presented with step-by-step solutions.

Example: First proof shows triangle EFG congruent to triangle GHE using SSS postulate, utilizing given conditions EF ≅ GH and FG ≅ HE, along with the reflexive property for GE.

Highlight: Second proof demonstrates triangle DRA congruent to triangle DRG using SAS postulate, incorporating right angles and the reflexive property.

Page 3: Advanced Proofs and Hypotenuse-Leg Theorem

This page introduces the Hypotenuse-Leg (HL) Congruence Theorem and continues with more complex proof examples.

Definition: The Hypotenuse-Leg Congruence Theorem states that if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Example: A proof involving triangles NOT and RSP demonstrates the application of given conditions and theorem principles.

Page 4: ASA and AAS Congruence

This page explores two additional triangle congruence theorems: Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS).

Definition: ASA Congruence states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Definition: AAS Congruence establishes that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Page 5: CPCTC Theorem Application

This page focuses on the CPCTC theorem and its practical application in geometric proofs.

Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a theorem stating that when two triangles are proven congruent, all their corresponding parts are also congruent.

Example: A detailed proof showing JK = JL using angle bisector JM and the ASA theorem, followed by CPCTC application.

Page 6: Extended Proofs

This page provides additional practice with extended proofs, incorporating various concepts learned throughout the unit.

Highlight: The proof combines multiple concepts including vertical angles, midpoint properties, and the CPCTC theorem.

Example: A complex proof involving parallel lines, midpoints, and triangle congruence is presented with detailed steps and reasons.

Page 1: Triangle Congruence Fundamentals

This page introduces the fundamental concepts of triangle congruence, focusing on the SSS and SAS postulates. The content establishes the groundwork for understanding how to prove triangles are congruent using different methods.

Definition: Triangle congruence occurs when all six pairs of corresponding parts between two triangles are equal.

Highlight: Two primary postulates involve sides (SSS and SAS), while one theorem specifically applies to right triangles.

Vocabulary: SSS (Side-Side-Side) - A postulate stating that if all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: The reflexive property of congruence is demonstrated when there is a shared side between triangles, and vertical angles are shown to be equal.