PROOFS with Congruent triangles

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states 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 Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is being compared to triangle ABC, they are congruent by the Reflexive Property.

Front

What is the CPCTC Theorem?

Back

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

Front

What is the SSS postulate?

Back

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

Front

What is the ASA postulate?

Back

ASA stands for Angle-Side-Angle, a postulate that states 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 Vertical Angles Theorem?

Back

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

Front

What are Alternate Interior Angles?

Back

Alternate Interior Angles are pairs of angles that are on opposite sides of a transversal and inside two parallel lines. If the lines are parallel, these angles are congruent.

Front

What is the definition of congruent triangles?

Back

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

Front

What is the significance of the Transitive Property in geometry?

Back

The Transitive Property states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third. This is often used in proofs.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that if a point lies on the bisector of an angle, it is equidistant from the two sides of the angle.