Triangle Congruence Criteria and Definitions

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 SSS stand for in triangle congruence?

Back

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

Back

AAS stands for Angle-Angle-Side, a theorem 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 theorem that states 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

What is the congruence statement for triangles ΔABC and ΔDEF if they are congruent by ASA?

Back

ΔABC ≅ ΔDEF.

Tags

CCSS.HSG.CO.B.7

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

What is the difference between SSA and AAS in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, while AAS (Angle-Angle-Side) does guarantee triangle congruence.

Tags

CCSS.HSG.SRT.B.5

Front

Can AAA (Angle-Angle-Angle) prove triangle congruence?

Back

No, AAA only shows that triangles are similar, not necessarily congruent.

Tags

CCSS.8.G.A.2

Front

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

Back

The included angle is the angle formed between the two sides being compared, and it is crucial for establishing congruence.

Tags

CCSS.HSG.SRT.B.5