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:	Quadrilateral ABCD with $∠ A ≅ ∠ C$ and $∠ B ≅ ∠ D$
Prove:	Quadrilateral ABCD is a parallelogram.

Choices:

a.	$2 (m ∠ A + 2 m ∠ B) = 360^{\circ}$
b.	Substitution Property of Equality
c.	$∠ B$ and $∠ C$ are supplementary.
d.	$2 m ∠ B + 2 m ∠ C = 360^{\circ}$
e.	$m ∠ B = m ∠ D$
f.	Definition of parallelogram

g.	Definition of same-side interior angles
h.	$∠ B$ and $∠ C$ are same-side interior angles.
i.	Definition of supplementary angles
j.	Division Property of Equality
k.	Converse of Same-Side Interior Angles Theorem
l.	The sum of the measures of the interior angles of a convex polygon with n sides is equal to $(n - 2) 180^{\circ} .$

Proof:

Statements

Reasons

1. Quadrilateral ABCD with

∠ A ≅ ∠ C

and

∠ B ≅ ∠ D

1. Given

m ∠ A = m ∠ C

2. Definition of congruent angles

m ∠ A + m ∠ B + m ∠ C + m ∠ D

= 360^{\circ}

m ∠ A + m ∠ B + m ∠ A + m ∠ B

= 360^{\circ}

m ∠ C + m ∠ B + m ∠ C + m ∠ B

= 360^{\circ}

2 m ∠ A + 2 m ∠ B = 360^{\circ}

5. Addition Property of Equality

2 (m ∠ B + 2 m ∠ C) = 360^{\circ}

6. Distributive Property

m ∠ A + m ∠ B = 180^{\circ}

m ∠ B + m ∠ C = 180^{\circ}

∠ A

and

∠ B

are same-side interior angles.

∠ A

and

∠ B

are supplementary.

10.

\bar{B C} ∥ \bar{A D}

\bar{A B} ∥ \bar{C D}

10.

11. Quadrilateral ABCD is a parallelogram.

11.

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