Triangle Congruence

Front

What is a triangle?

Back

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Tags

CCSS.2.G.A.1

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

What are the three main criteria for triangle congruence?

Back

1. Side-Side-Side (SSS) - All three sides are equal. 2. Side-Angle-Side (SAS) - Two sides and the included angle are equal. 3. Angle-Side-Angle (ASA) - Two angles and the included side are equal.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The SAS Congruence 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 Angle-Side-Angle (ASA) Congruence Postulate?

Back

The ASA Congruence 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 Angle-Angle-Side (AAS) Congruence Theorem?

Back

The AAS Congruence 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 Hypotenuse-Leg (HL) Congruence Theorem?

Back

The HL Congruence 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

How can you prove triangles are congruent using transformations?

Back

You can prove triangles are congruent by showing that one triangle can be transformed into another using rigid motions such as translations, rotations, and reflections.

Tags

CCSS.HSG.SRT.B.5

Front

What is the importance of triangle congruence in real life?

Back

Triangle congruence is important in various fields such as architecture, engineering, and art, as it helps in creating structures and designs that are stable and aesthetically pleasing.

Tags

CCSS.8.G.A.2