5.4 Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning all corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

What does the Reflexive Property state?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning AB = AB.

Front

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

Back

The SAS Postulate 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.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The SSS Postulate states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The ASA Postulate 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.

Tags

CCSS.HSG.SRT.B.5

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Theorem 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.

Tags

CCSS.HSG.SRT.B.5

Front

What is the HL (Hypotenuse-Leg) Congruence Theorem?

Back

The HL Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the Vertical Angle Theorem?

Back

The Vertical Angle Theorem states that vertical angles are congruent, meaning if two angles are opposite each other when two lines intersect, they are equal.

Tags

CCSS.HSG.CO.C.9

Front

What is CPCTC?

Back

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

Tags

CCSS.HSG.CO.B.7

Front

What is the Transitive Property?

Back

The Transitive Property states that if a = b and b = c, then a = c. This property is often used in proofs to show relationships between congruent figures.