Lesson 6 triangle proofs quick check

Answer 1

To help you with Lesson 6 on triangle proofs, I can provide a summary of key concepts related to triangle proofs, which can include various theorems, properties, and types of proofs.

Here are some common methods and theorems used in triangle proofs:

1. Triangle Congruence Theorems:

   • SSS (Side-Side-Side): If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
   • SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
   • ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
   • AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.
   • HL (Hypotenuse-Leg for right triangles): If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

2. Properties of Triangles:

   • The sum of the angles in a triangle is always 180 degrees.
   • The exterior angle of a triangle is equal to the sum of the two remote interior angles.

3. Proof Techniques:

   • Two-column proofs: A structured way to present a proof with statements on one side and corresponding reasons on the other.
   • Flowchart proofs: A diagrammatic way showing the flow of logical statements leading to the conclusion.
   • Paragraph proofs: A written explanation of the proof in paragraph form, outlining the main ideas in a coherent way.

4. Common Strategies:

   • Identify known congruent triangles and apply the congruence theorems.
   • Use corresponding parts of congruent triangles (CPCTC) to prove additional congruences.
   • Use angle relationships, such as vertical angles, complementary angles, and supplementary angles, to establish congruences or equalities.

If you're looking for specific questions or examples, please provide details, and I'd be happy to assist!