Geometry - 5.3 ASA and AAS

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

What is the difference between ASA and AAS?

Back

The difference is that ASA requires the included side between the two angles to be congruent, while AAS does not require the side to be included between the two angles.

Tags

CCSS.HSG.SRT.B.5

Front

If two triangles have two pairs of congruent angles and one pair of congruent sides, what can be concluded?

Back

The triangles are congruent by the AAS criterion.

Tags

CCSS.8.G.A.2

Front

What additional information is needed to prove triangles congruent by AAS?

Back

You need to know that one pair of corresponding non-included sides is congruent.

Tags

CCSS.HSG.SRT.B.5

Front

Can AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) does not prove congruence; it only shows that triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means all corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

How can you determine if two triangles are congruent using the AAS theorem?

Back

If two angles and a non-included side of one triangle are congruent 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 is the congruence statement for two congruent triangles?

Back

A congruence statement lists the corresponding vertices of congruent triangles in order, such as triangle ABC ≅ triangle DEF.

Tags

CCSS.HSG.CO.B.7

Front

What is the role of the included side in the ASA theorem?

Back

The included side is the side between the two angles being compared; it must be congruent for the triangles to be congruent by ASA.

Tags

CCSS.HSG.SRT.B.5