Column Proof Triangle Congruence

What is the reason for statement #1?

• Given

• Definition of Congruent Segments

• Prove

In this picture,

• <BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other

• <C=<C because they are vertical angles and vertical angles are always congruent to each other

• <EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other

• None of the above; we don't actually have vertical angles

What is the "statement" for step 3 of the proof?

• HA=HA

• HA=AH

• MA=AM

• MA=MA

Use the reasons below to complete the proof.

e

f

g

h

SSS

def of segment bisector

given

reflexive property

def of angle bisector

SAS

Vertical angles

angle addition

corresponding angles

What is statement #4?

• ∆HFG≅∆IHF

• ∆FHG≅∆IHF

• ∆GFH≅∆IFH

• ∆HFG≅∆IFH

What is statement #2?

• ∠ABC≅∠EDC

• ∠BCA≅∠DCE

• BC≅CD

• ∠E≅∠A

What is the "statement" for step 3 of the proof? 

• ∡EDA≅∡DCB

• ∡AED≅∡BEC

• DE=CE

• ∡AED≅∡CED

Fill in the two missing steps in the proof.

• Transitive Property, SAS (Side-Angle-Side)

• Reflexive Property, SAS (Side-Angle-Side)

• Reflexive Property, Vertical Angles Theorem

• Transitive Property, SSS (Side-Side-Side)

GOLF FLAGS Each hole on a golf course is marked with a triangular flag, as shown in the picture. Points F, G, and H mark the vertices of the flag, and KH bisects ∠GHF and is a perpendicular bisector of GF. Write a two-column proof to prove that GH ≅ FH. Given: KH bisects ∠GHF, KH is a perpendicular bisector of GF. Prove: GH ≅ FH.

Evaluate responses using AI:

OFF

What is statement #1?

• BC≅DC

• AC≅EC

• BC≅DC, AC≅EC

• ∆BCA≅∆DCE