Congruent Triangle Proofs

Front

What is a congruent triangle?

Back

Triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

What is the Reflexive Property?

Back

A property stating that any geometric figure is congruent to itself (e.g., segment AB ≌ segment AB).

Front

What is the Segment Bisector?

Back

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

Front

What are Alternate Interior Angles?

Back

Angles that are on opposite sides of a transversal and inside the two lines it intersects; they are congruent when the lines are parallel.

Front

What are Vertical Angles?

Back

Angles that are opposite each other when two lines intersect; they are always congruent.

Front

What is the definition of Midpoint?

Back

The point that divides a segment into two equal parts.

Front

What is the purpose of congruence statements?

Back

To show that two triangles are congruent by listing corresponding parts in a specific order.

Front

What is the Angle-Side-Angle (ASA) Congruence Postulate?

Back

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the Side-Angle-Side (SAS) Congruence Postulate?

Back

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.