Proofs of Triangle Congruences

What is the justification?

• Definition of congruence

• Reflexive Property of Congruence

• Segment Addition Postulate

• Definition of Midpoint

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Which of the following is a correct statement and reason for the proof shown?

Given the information in the image, you can deduce that the triangles are ​ (a)   because ​ (b)   ​

• of the ASA Triangle congruence postulate.

• of the SSA Triangle congruence theorem.

• of the SSS Triangle congruence postulate.

• of the HL Triangle congruence postulate.

• of the AAS Triangle congruence theorem.

• of the SAS Triangle congruence theorem.

• there is not enough information given.

• congruent

• not congruent

Fill in the proof with the labels below.

f

g

h

b

c

e

i

a

d

j

CPCTC

SM

Definition of midpoint

∠SMR

∠SEM

△SEM ≅ △KMR

AAS congruence theorem

RM ≅ EM

Alternate internal ∠’s are ≅

SAS congruence postulate

What additional information is needed to prove that △MYG ≅ △MYR?​ ​ (a)  

• EO ≅ TE

• ∠YTE ≅ ∠YES

• ∠ESO ≅ ∠TES

• GM ≅ MK

• GR ≅ GR

• OT ≅ ZE

• ∠OMS ≅ ∠MSE