ASA & AAS Theorem

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem 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 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 a corresponding non-included side of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SAS theorem?

Back

SAS stands for Side-Angle-Side, a theorem 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 is the SSS theorem?

Back

SSS stands for Side-Side-Side, a theorem 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

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, you need to show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove triangles are congruent using AAS?

Back

To prove triangles are congruent using AAS, you need to show that two angles and a non-included side of one triangle are equal to two angles and a 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 equal, while AAS does not require the side to be included between the two angles.

Front

Can you use ASA or AAS to prove triangles are congruent if only one angle is known?

Back

No, you need at least two angles and the corresponding side (for ASA) or two angles and a non-included side (for AAS) to prove congruence.

Tags

CCSS.HSG.SRT.B.5

Front

What is an example of using the ASA theorem?

Back

If triangle ABC has angles A and B equal to angles D and E in triangle DEF, and side AB is equal to side DE, then triangle ABC is congruent to triangle DEF by ASA.

Tags

CCSS.HSG.SRT.B.5

Front

What is an example of using the AAS theorem?

Back

If triangle XYZ has angles X and Y equal to angles P and Q in triangle RST, and side YZ is equal to side QT, then triangle XYZ is congruent to triangle RST by AAS.

Tags

CCSS.HSG.SRT.B.5