Congruent Triangles

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states 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 SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states 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 does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states 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 HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a postulate that applies to right triangles, stating 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 triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

If two triangles have two pairs of equal angles, what can be concluded about the triangles?

Back

The triangles are congruent by the AAS postulate.

Tags

CCSS.HSG.SRT.B.5

Front

If two triangles have two pairs of equal sides and the included angle is equal, what can be concluded about the triangles?

Back

The triangles are congruent by the SAS postulate.

Tags

CCSS.HSG.SRT.B.5

Front

Can two triangles be congruent if only two sides are equal and the angle opposite one of the sides is not equal?

Back

No, the triangles cannot be concluded as congruent; this is known as the SSA condition, which does not guarantee congruence.

Tags

CCSS.8.G.A.2

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle is crucial in the SAS postulate because it is the angle formed between the two sides being compared, ensuring the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5