EDGE Math 8

Identify the missing statement or reason to complete the two-column proof. Type the letter of your answer in each blank.

Given:	$\bar{LI} ∥ \bar{KE}$ $\bar{LE} ≅ \bar{IK}$
Prove:	Quadrilateral LIKE is a parallelogram.

Choices:

a.	$\bar{LI} ≅ \bar{KE}$
b.	Definition of congruent angles
c.	SAS Congruence Postulate
d.	Consecutive angles in a parallelogram are supplementary.

e.	$\bar{LK} ≅ \bar{LK}$
f.	Alternate Interior Angles Theorem
g.	$\bar{IK} ≅ \bar{IK}$
h.	If two sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Proof:

Statements

Reasons

\bar{LI} ∥ \bar{KE}

\bar{LE} ≅ \bar{IK}

1. Given

∠ I L K ≅ ∠ L K E

2. Construction and

3. Reflexive Property of Segment Congruence

Δ I L K ≅ Δ L K E

5. CPCTC

5. Quadrilateral LIKE is a parallelogram.

6. Statements 1 and 5, and

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