Unit 4: Triangles & Congruence

Objective: To determine if a triangle can exist and to compare side lengths and angle measures.

Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Side-Angle Relationship: In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Objective: To find missing angle measures in triangles.

Triangle Angle Sum Theorem: The three interior angles of any triangle always add up to 180°.

Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Objective: To prove triangles are congruent using SSS, SAS, and ASA postulates.

Congruent Triangles: Triangles that have the exact same size and shape. All corresponding sides and angles are equal.

• SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another.
• SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to those of another.
• ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to those of another.

Objective: To use congruence postulates to prove triangles are congruent in algebraic and coordinate problems.

We use the congruence postulates (SSS, SAS, ASA, etc.) as reasons in proofs to show two triangles are identical. Once triangles are proven congruent, we know that their corresponding parts are also congruent (CPCTC).

This can be applied on the coordinate plane by using the distance formula (to find side lengths) and slope formula (to find right angles).