SSS, HL, and SAS Review

Chapter 5.3 and 5.5

SSS, HL, and SAS Review

Multiple Select

What three triangle congruences do we know so far?

• SAS

• SAA

• SSS

• HL

Included Angle

Angle D is the included angle of side ED and FD.

Angle A is the included angle of side BA and CA. ​

​​

The included angle means the angle between two sides. In other words it is the angle 'included between' two sides.

Multiple Choice

What is the included angle between sides AB and CB?

• $$\angle A$$

• $$\angle B$$

• $$\angle C$$

Multiple Choice

What is the included angle between sides AC and BC?

• $$\angle A$$

• $$\angle B$$

• $$\angle C$$

Vertical Angles ​

Don't forget about some of our hidden relationships....

Multiple Choice

In this picture,

• <BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other
• <C=<C because they are vertical angles and vertical angles are always congruent to each other
• <EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other
• None of the above; we don't actually have vertical angles

Draw

Are there any congruent angles in this diagram?

​Side - Side - Side (SSS)

​SSS allows us to prove triangles congruent if...

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.

Reflexive Property of Congruence

​Whenever two triangles share a side, instantly think of Reflexive Property of Congruence!

​CA is congruent to CA by the Reflexive Property of Congruence

Multiple Choice

Which triangle congruence theorem proves the two triangles congruent?

• SAS

• SSS

• not enough information

Multiple Choice

Which triangle congruence theorem proves the two triangles congruent?

• SSS

• SAS

• not enough information

Multiple Choice

Which triangle congruence theorem proves the two triangles congruent?

• SAS

• Not enough information

• SSS

Multiple Choice

Are these triangles congruent?

• Yes, by ASA
• Yes, by SAS
• Yes, by AAS
• No, this is the SSA one!!

Multiple Choice

ΔLMO ≅ _______ by ______

• ΔNOM , SSS

• ΔMON , SSS

• ΔNOM , SAS

• Cannot Be Determined

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by AAS

• Not congruent

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by AAS

• Yes - by ASA

• Yes - by HL

• Yes - by SAS

• Not congruent

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by AAS

• Yes - by ASA

• Yes - by HL

• Yes - by SAS

• Not congruent

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• ASA
• SSA
• HL

Multiple Choice

Which of the following did we not learn to prove triangles congruent?

• HL
• AAA
• SSS
• SAS