SSS, SAS, and SSA Congruence Shortcuts

Objectives:

1. Explore shortcuts for determining whether triangles are congruent.

SSS, SAS, and SSA Congruence Shortcuts

Objectives:

2. Discover whether SSS, SAS, and SSA are valid shortcuts.

(SSS Congruence Conj.)If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

Are these triangles congruent?

Yes–(SSS Congruence Conj.)

Are these triangles congruent?

NO

Are these triangles congruent?

Yes–(SSS Congruence Conj.)

(SAS Congruence Conj.)If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Are these triangles congruent?

Yes–(SAS Congruence Conj.)

Are these triangles congruent?

NO

Are these triangles congruent?

Yes–(SAS Congruence Conj.)

(SSA Congruence Conj.)SSA does not necessarily prove triangle congruence.

We do not use SSA to prove triangle congruency!!!

Think about the shortcuts you learned today that prove

triangle congruence.

SSS & SAS

Which shortcut talked about today does not necessarily prove triangle congruency?

SSA

ASA, SAA, AAA Congruence Shortcuts?

Objectives:1. Discover whether ASA, SAA, and AAA are valid shortcuts for determining whether triangles are .

C-35 (ASA Congruence Conj.): If 2 ’s and the side between them in one triangle are congruent to 2 ’s and the side between them in another triangle, then the triangles are .

Are these triangles congruent?

Yes–(ASA Congruence Conj.)

Are these triangles congruent?

NO

Are these triangles congruent?

NO

(SAA Congruency Conj.):

SAA proves triangle

congruency!

Are these triangles congruent?

Yes–(SAA Congruence Conj.)

Are these triangles congruent?

NO

Are these triangles congruent?

NO

AAA does not necessarily prove

triangle congruency.

Are these triangles congruent?

NO

Are these triangles congruent?

Yes!! (AAA)