Triangle Congruence

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are considered 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 are the criteria for triangle congruence?

Back

The criteria for triangle congruence include: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Tags

CCSS.HSG.SRT.B.5

Front

What does the SSS criterion state?

Back

The SSS (Side-Side-Side) criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Tags

CCSS.8.G.A.2

Front

What does the SAS criterion state?

Back

The SAS (Side-Angle-Side) 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, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does the ASA criterion state?

Back

The ASA (Angle-Side-Angle) 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, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does the AAS criterion state?

Back

The AAS (Angle-Angle-Side) 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, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does the HL criterion state?

Back

The HL (Hypotenuse-Leg) criterion states that 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 two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

If ∆ABC ≅ ∆LMN, what can we conclude about their corresponding angles?

Back

If ∆ABC ≅ ∆LMN, then ∠A ≅ ∠L, ∠B ≅ ∠M, and ∠C ≅ ∠N.

Tags

CCSS.HSG.CO.B.7

Front

If two triangles are congruent, what can we say about their corresponding sides?

Back

If two triangles are congruent, then their corresponding sides are equal in length.

Tags

CCSS.8.G.A.2

Front

What is the significance of the congruence statement ∆ISR ≅ ∆TRS?

Back

The congruence statement ∆ISR ≅ ∆TRS indicates that the triangles ISR and TRS are congruent, meaning their corresponding sides and angles are equal.

Tags

CCSS.HSG.CO.B.7