Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The main criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which 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 AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning for any triangle ABC, triangle ABC ≅ triangle ABC.

Front

What is a segment bisector?

Back

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

Front

What is the definition of vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

Front

What is the significance of the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.