Page 3: Homework - ASA and AAS Proofs

This page provides homework exercises focusing on Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruence proofs. It includes detailed instructions and space for students to complete the proofs step-by-step.

Example: Proof 1 demonstrates the use of ASA to prove ΔABD ≅ ΔCBD, given that BD bisects ∠ABC and ∠BDA = ∠BDC.

Highlight: The proofs require students to apply their knowledge of angle bisectors, alternate interior angles, and vertical angles in addition to the congruence theorems.

Vocabulary: Bisect - to divide into two equal parts.

Page 1: Right Triangle Congruence Proofs HL

This page introduces the HL (hypotenuse-leg) Congruence Theorem and provides examples of its application. It explains that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent. The page includes visual representations of right triangles and step-by-step proofs using the HL Theorem.

Definition: The hypotenuse is the longest side of a right triangle, opposite the right angle. A leg is a side adjacent to the right angle.

Example: A proof is provided to show that ΔLMP ≅ ΔNMP using the HL Theorem, given that LM = MN and MP is common to both triangles.

Highlight: The page also demonstrates an alternative method using the AAS (Angle-Angle-Side) congruence theorem, showcasing the versatility of triangle congruence proofs.