Triangle Congruence Practice

Front

Which Triangle Congruence Theorem proves these triangles congruent? Options: AAS, ASA, SAS, HL, Cannot be proven congruent

Back

ASA

Answer explanation

These triangles are congruent by ASA.

Angle-Side-Angle

Front

Which Triangle Congruence Theorem proves these triangles congruent? Options: AAS, ASA, SAS, SSS, Cannot be proven congruent

Back

SSS

Answer explanation

Mark the shared side as congruent. Then we can see the triangles are congruent by SSS.

Side-Side-Side

Front

Which Triangle Congruence Theorem proves these triangles congruent? Options: AAS, ASA, SSA, HL, Cannot be proven congruent

Back

AAS

Answer explanation

First, mark the vertical angles as congruent.

-------------

Then, focus on one triangle and see Angle-Angle-Side.

AAS

This is not ASA because the Side is NOT between the angles.

Front

Which Triangle Congruence Theorem proves these triangles congruent? Options: AAS, SAS, ASA, SSS

Back

ASA

Answer explanation

First, mark the shared side as congruent.

Then, focus on just one of the triangles if you need to.

These triangles are congruent by Angle-Side-Angle.

ASA

Front

Which Triangle Congruence Theorem proves these triangles congruent?

AAA

,

ASA

,

AAS

,

Cannot be proved congruent!

Back

Cannot be proved congruent!

Answer explanation

Even though all the angles are marked congruent, AAA, Angle-Angle-Angle is NOT a triangle congruence theorem.

This cannot prove triangles are congruent.

Remember "No screaming! AAA!!!"

Front

For which situation could you prove ∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem? Options: I only, II only, III only, I and III

Back

III only

Answer explanation

The hypotenuses are only marked as congruent in the third picture.

Front

How are the triangles congruent? Options:

SAS

,

SSA

,

ASA

,

These are not congruent

Back

These are not congruent

Answer explanation

Even though both triangles have two sides and one angle marked congruent, they are not in the same order.

SAS is not congruent to SSA, so these triangles cannot be proven congruent.

Front

Are these triangles congruent?

Back

Yes, by HL

Answer explanation

Once we mark the shared side as a congruent leg, we can see they are congruent by HL (Hypotenuse-Leg).

Front

Are these triangles congruent? Options:

Yes, by AAS

,

Yes, by SAS

,

Yes, by ASA

,

No, this is the SSA one!!

Back

No, this is the SSA one!!

Answer explanation

Even though Side-Side-Angle are marked congruent, SSA is NOT a triangle congruence theorem.

This cannot prove triangles are congruent.

Remember "No swearing!"

Front

Are the triangles congruent?

Back

Yes, by SAS

Answer explanation

Since the second triangle does not have the third side marked as a congruent pair, we can only use SAS.

Side-Angle-Side