EDGE Math 8

Identify the missing statements or reasons that will complete the two-column proof. Type the letter of your answer in each blank.

Given:	$Δ T R O$ is an isosceles triangle with $∠ O$ as vertex. $\bar{T R} ∥ \bar{I G}$
Prove:	$Δ I G O$ is an isosceles triangle.

Choices:

g.	Definition of isosceles triangle
h.	Transitive Property of Angle Congruence
i.	Vertical Angles Theorem
j.	Converse of the Isosceles Triangle Theorem
k.	Isosceles Triangle Theorem
l.	Reflexive Property of Equality

Proof:

Statements

Reasons

Δ T R O

is an isosceles triangle with

∠ O

as vertex.

\bar{T R} ∥ \bar{I G}

1. Given

\bar{T O} ≅ \bar{O R}

∠ R T O ≅ ∠ T R O

∠ R T O ≅ ∠ G I O

and

4. If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

∠ G I O ≅ ∠ I G O

\bar{I O} ≅ \bar{G O}

Δ I G O

is an isosceles triangle.

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