TRIANGLE CONGRUENCE AND CPCTC

Which Triangle Congruence Theorem proves these triangles congruent?

• AAS

• ASA

• SAS

• HL

• Cannot be proven congruent

Answer explanation

These triangles are congruent by ASA.

Angle-Side-Angle

Which Triangle Congruence Theorem proves these triangles congruent?

• AAS

• ASA

• SAS

• SSS

• Cannot be proven congruent

Answer explanation

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

Side-Side-Side

Which Triangle Congruence Theorem proves these triangles congruent?

• AAS

• ASA

• SSA

• HL

• Cannot be proven congruent

Answer explanation

First, mark the vertical angles as congruent.

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

AAS

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

Which Triangle Congruence Theorem proves these triangles congruent?

• AAS

• SAS

• ASA

• SSS

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

Which Triangle Congruence Theorem proves these triangles congruent?

• AAA

• ASA

• AAS

• 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!!!"

For which situation could you prove

∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem?

Answer explanation

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

How are the triangles congruent?

• SAS

• SSA

• ASA

• 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.

Are these triangles congruent?

• Yes, by AAS

• Yes, by HL

• Yes, by SAS

• No, these are not congruent

Answer explanation

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

Are these triangles congruent?

• Yes, by AAS

• Yes, by SAS

• Yes, by ASA

• 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!"

Are the triangles congruent?

• Yes, by SSA

• Yes, by HL

• Yes, by SSS

• Yes, by SAS

• Not enough information

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