Triangle Proofs Review

What is #4 Statement?

• ∠MNL ≌ ∠ONP

• MN ≌ ON

• N ≌ N

• MO ≌ OM

What is #2 Reason?

• Same Line

• Reflexive Property

• Segment Bisector

• Definition of Midpoint

What is #3 Reason?

• Same Line

• Perpendicular Lines

• Segment Bisector

• Reflexive Property

What is #5 Statement?

• ∠QPR ≌ ∠STR

• ∠PQR ≌ ∠STR

• ∠QRP ≌ ∠TSR

• ∠QRP ≌ ∠TRS

Are the triangles congruent?

Given: ZX bisects angle WXY.

ZX is perpendicular to WY

• Yes, AAS

• Yes, ASA

• Yes, SSA

• No

Answer explanation

ZX is congruent to ZX through the reflexive property.

Angle WXZ is congruent to angle YXZ through the angle bisector rule.

Angle WZX and angle YZX are congruent because they are both right angles.

Therefore, the triangles are congruent through ASA

Are the triangles congruent?

Given: PX = TY

Angle QPX = angle STY

Angle RXY = angle RYX

• Yes, SSS

• Yes, AAA

• No

• Yes, ASA

Answer explanation

PY = TX because PX = TY (given) and XY =XY through reflexive.

Angle QPX = angle STY (given)

Angle RXY = angle RYX (given)

Therefore, the triangles are congruent through ASA

Are these triangles congruent?

DF = GE

• Yes, SSA

• Yes, ASA

• Yes, SSS

• No

Answer explanation

DF = GE and DE = GF (given)

EF = EF through the reflexive property

Are these triangles congruent?

Given: AE = CD

B bisects AD

• Yes, SSA

• Yes, SSS

• Yes, AAA

• No

Answer explanation

Angle ABE = angle DBC as vertical angles.

AB = DB through the bisector rule.

AE = CD (given)

However, SSA does NOT prove triangles are congruent.

Are these triangles congruent?

Given: AB = DE

C bisects AE and BD

• Yes, AAA

• Yes, SSS

• Yes, SSA

• No

Answer explanation

AB = DE (given)

AC = CE and DC = CB through the bisector rule.

Therefore, the triangles are congruent through SSS.

Are the triangles congruent?

Given: ZX bisects angle WXY.

WX = YX

• Yes, SAS

• Yes, AAS

• Yes, SSA

• No

Answer explanation

Angle WXZ = angle YXZ through the bisector rule.

ZX = ZX through reflexive property

WX = YX (given)

Therefore, the triangles are congruent through SAS