Basic Triangle Congruence Proofs

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

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

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 HL Triangle congruence postulate.

• of the AAS Triangle congruence theorem.

• of the SAS Triangle congruence theorem.

• there is not enough information given.

• congruent

• not necessarily congruent

• of the SSS Triangle congruence postulate.

You are trying to prove △MXC≅△LXC. Identify the components of the triangles on the diagram that are congruent due to the reflexive property help prove their congruence by selecting the points which define the components.

Fill in the proof with the labels below.

f

g

h

b

c

e

i

a

d

j

RM ≅ EM

SM

Definition of midpoint

△SEM ≅ △KMR

SAS congruence postulate

∠SEM

CPCTC

∠SMR

Alternate internal ∠’s are ≅

AAS congruence theorem

Given the image, mark all true statements

• ∠SEO ≅ ∠STZ

• EO ≅ TZ

• SO ≅ SZ

• ∠ESO ≅ ∠TZS

• ∠YTE ≅ ∠YES

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

Mark the angle pairs which are congruent due to the presence of transversal HK which would help prove that triangles RXH and KXN are congruent.

• ∠RXK ≅ ∠HXN

• ∠RHX ≅ ∠NKX

• ∠CRN ≅ ∠TNC

• ∠RHX ≅ ∠KXN

You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you would mark the blue, single arc angles congruent?

• The two angles are corresponding parts of the two triangles in question.

• Alternate internal angles of a transversal are congruent.

• The reflexive property of congruence.

• The transversal cuts through two parallel lines.

• These angles are Vertical angles and therefore are congruent

You are trying to prove triangles A and B congruent. Given the information depicted on the diagram. What is the reason you would mark the blue, single arc angles congruent?

• The two angles are corresponding parts of the two triangles in question.

• Alternate internal angles of a transversal are congruent.

• The reflexive property of congruence.

• These angles are Vertical angles and therefore are congruent.

• It meets the criteria for the angle addition postulate.