4.6: Congruence in Overlapping Triangles

Front

What does it mean for two triangles to be congruent?

Back

Two 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 is the SSS (Side-Side-Side) congruence criterion?

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

What is the ASA (Angle-Side-Angle) congruence criterion?

Back

The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the AAS (Angle-Angle-Side) congruence criterion?

Back

The AAS criterion 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, the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SAS (Side-Angle-Side) congruence criterion?

Back

The SAS criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the HL (Hypotenuse-Leg) congruence criterion?

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

What is an overlapping triangle?

Back

Overlapping triangles share a common side or angle, which can be used to establish congruence between them.

Tags

CCSS.8.G.A.2

Front

Identify a common side or angle in overlapping triangles.

Back

A common side or angle is a side or angle that is shared between the two triangles, such as side XY in triangles XYZ and XZW.

Tags

CCSS.8.G.A.2

Front

What is the significance of common angles in overlapping triangles?

Back

Common angles help establish the congruence of overlapping triangles by providing equal measures that can be used in congruence criteria.

Tags

CCSS.8.G.A.2

Front

How can you identify common parts in overlapping triangles?

Back

Common parts can be identified by looking for shared sides or angles between the triangles.

Tags

CCSS.2.G.A.1