Triangle Congruence Proofs

Front

What is the Midpoint Theorem in triangle congruence?

Back

The Midpoint Theorem states that if a point M is the midpoint of segment AB, then AM is congruent to MB (i.e., AM ≅ MB). This theorem is often used in proofs involving triangle congruence.

Front

What does it mean for two angles to be congruent?

Back

Two angles are congruent if they have the same measure. This is denoted as ∠A ≅ ∠B.

Front

What is the Reflexive Property of Congruence?

Back

The Reflexive Property of Congruence states that any geometric figure is congruent to itself. For example, segment AB is congruent to segment AB (AB ≅ AB).

Front

What is the definition of a bisector in geometry?

Back

A bisector is a line, segment, or ray that divides an angle or segment into two equal parts.

Front

What does CPCTC stand for in triangle congruence?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is used to prove that corresponding sides and angles of congruent triangles are also congruent.

Front

What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. Congruent figures can be transformed into one another through rotations, translations, and reflections.

Front

What is the significance of the Angle-Angle (AA) criterion for triangle similarity?

Back

The Angle-Angle (AA) criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

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

Back

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

Front

What is the Side-Side-Side (SSS) criterion for triangle congruence?

Back

The Side-Side-Side (SSS) criterion states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.