Practice Triangle Congruence

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

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.HSG.SRT.B.5

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.

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.HSG.SRT.B.5

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!!!"

Tags

CCSS.HSG.SRT.B.5

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).

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.HSG.SRT.B.5

What does CPCTC stand for?

• Colorful Pieces of Careful Tarantulas are Congruent

• Congruent Parts of Cognizant T-Rexes are Charming

• Corresponding Parts of Congruent Triangles are Congruent

Answer explanation

Tarantulas and T-Rexes are excited because once we prove triangles are congruent, we know ALL

Corresponding Parts of Congruent Triangles are Congruent!

Tags

CCSS.HSG.SRT.B.5

What is the reason for statement #2?

• CPCTC

• Given

• Reflexive Property

• Definition of Midpoint

Answer explanation

Like looking in a mirror and seeing your REFLECTION, segment KM is congruent to itself!

Tags

CCSS.HSG.SRT.B.5

What is the reason for statement #3? (How do we know these triangles are congruent?)

• CPCTC

• Reflective Property

• SAS

• SSS

Answer explanation

Focus on just one of the triangles if you need to.

All three sides were marked so these triangles are congruent by SSS.

Side-Side-Side

Tags

CCSS.HSG.SRT.B.5