Unit 3: Congruent Triangle Proofs Practice

What is statement #1?

• BC≅DC

• AC≅EC

• BC≅DC, AC≅EC

• ∆BCA≅∆DCE

Answer explanation

We know that both of the givens must be listed in the first step because there is no other line later in the proof that states a given.

Since every given needs to be listed in the proof, they must have both been included in the first step.

Tags

CCSS.HSG.SRT.B.5

What is statement #2?

• ∠ABC≅∠EDC

• ∠BCA≅∠DCE

• ∠E≅∠A

Answer explanation

Be sure to name your angles properly!

Tags

CCSS.HSG.CO.B.7

What is reason #3?

• SAS

• ASA

• SSS

• AAS

Answer explanation

There are two sets of congruent sides and one set of congruent angles, and the angle IS in the correct place for SAS!

Tags

CCSS.HSG.SRT.B.5

What is reason #1?

• Reflexive Property

• Definition of Bisect

• Prove

• Given

Answer explanation

A given is ALWAYS the first thing in a proof! :)

Tags

CCSS.HSG.SRT.B.5

What is reason #2?

• Definition of Midpoint

• Definition of Segment Bisector

• Definition of Angle Bisector

• Definition of Right Triangle

Answer explanation

"Bisect" is a word we should always explain in a proof. When we explain it, we use its definition in the next step.

An angle bisector creates two smaller congruent angles.

Tags

CCSS.HSG.CO.C.9

What is statement #3?

• FH≅FH

• GF≅GF

• IH≅IH

• GF≅FI

Answer explanation

Shared parts are congruent to themselves! :)

Tags

CCSS.HSG.SRT.B.5

What is statement #4?

• ∆HFG≅∆IHF

• ∆HFG≅∆HIF

• ∆GFH≅∆IFH

• ∆HFG≅∆IFH

Answer explanation

Your last statement should be an EXACT copy of your proof statement!

Be sure to keep corresponding parts lined up when writing a congruence statement.

Tags

CCSS.HSG.SRT.B.5

What is reason #4?

• ASA

• SAS

• HL

• AAS

Answer explanation

Two sets of angles are congruent, as well as the side that does NOT connect the congruent angles.

Tags

CCSS.HSG.SRT.B.5

What is statement #1?

• AB≅DC

• AC≅AC

• AB∥DC

• ∠A≅∠C

Answer explanation

The first statement should always be a given, and since Line 3 also will reference a given, we will only list one of the givens on Line 1.

Line 2 references some congruent angles that we can find from knowing we have parallel lines. Therefore, the given that references parallel lines must have preceded it in Line 1.

Tags

CCSS.HSG.CO.C.11

What is reason #2?

• Vertical angles are congruent.

• Consecutive angles are congruent.

• Alternate interior angles are congruent.

• Definition of Bisect

Answer explanation

Those angles are between the parallel lines and on opposite sides of the transversal.

Tags

CCSS.HSG.SRT.B.5