Congruent Triangle Proofs

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

What does the SAS (Side-Angle-Side) theorem state?

Back

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 does the ASA (Angle-Side-Angle) theorem state?

Back

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 does the AAS (Angle-Angle-Side) theorem state?

Back

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 does the SSS (Side-Side-Side) theorem state?

Back

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 HL (Hypotenuse-Leg) theorem?

Back

In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the Reflexive Property in triangle congruence?

Back

A property stating that a triangle is congruent to itself, often used in proofs.

Tags

CCSS.HSG.SRT.B.5

Front

What are Vertical Angles?

Back

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

Tags

CCSS.7.G.B.5

Front

What are Alternate Interior Angles?

Back

Angles that lie between two parallel lines and on opposite sides of a transversal; they are congruent.

Tags

CCSS.8.G.A.5

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which helps in proving triangle congruence.

Tags

CCSS.8.G.A.2