Congruent 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 their corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

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

Back

The SAS Congruence Theorem 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 two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The ASA Congruence Theorem 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 two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the AAS (Angle-Angle-Side) 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 a corresponding non-included side of another triangle, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The HL Congruence Theorem 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, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove two triangles are congruent using the SAS theorem?

Back

To prove two triangles are congruent using the SAS theorem, you need to show that two sides of one triangle are equal to two sides of the other triangle, and the angle between those sides is also equal.

Tags

CCSS.HSG.SRT.B.5

Front

What additional information is needed to prove triangles are congruent by HL?

Back

To prove triangles are congruent by HL, you need to show that the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, and one leg of one triangle is equal to one leg of the other.

Tags

CCSS.HSG.SRT.B.5

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size; their corresponding angles are equal, and their corresponding sides are proportional.

Tags

CCSS.8.G.A.2

Front

What is the importance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows us to use congruence theorems to prove that triangles are congruent.

Tags

CCSS.HSG.CO.B.7