Geometry: Congruent Triangles

Front

What is the Exterior Angle Theorem in geometry?

Back

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Front

What does the congruence statement \( \Delta FED \cong \Delta PQR \) imply about the triangles?

Back

It implies that the corresponding angles and sides of triangles FED and PQR are equal.

Front

What are the three main criteria for triangle congruence?

Back

The three main criteria for triangle congruence are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA).

Front

What is the Side-Angle-Side (SAS) congruence criterion?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the included angle is equal, then the triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) congruence criterion?

Back

The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the significance of the congruence statement \( \Delta ABC \cong \Delta DEF \)?

Back

It indicates that triangles ABC and DEF are congruent, meaning their corresponding sides and angles are equal.

Front

What is the definition of corresponding angles in congruent triangles?

Back

Corresponding angles in congruent triangles are angles that occupy the same relative position at each intersection where a straight line crosses two others.

Front

What is the definition of corresponding sides in congruent triangles?

Back

Corresponding sides in congruent triangles are sides that are in the same relative position in each triangle.

Front

What is the importance of knowing the missing angle or side in proving triangle congruence?

Back

Knowing the missing angle or side is crucial because it can help establish the necessary conditions (like SAS or ASA) to prove that two triangles are congruent.