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Type: Multiple-Choice
Category: Quadrilaterals
Level: Grade 10
Standards: HSG-CO.C.11
Score: 4
Author: nsharp1
Created: 6 years ago

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Quadrilaterals Question

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Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

What is the missing reason in step 4 of the following proof?

Given: Quadrilateral

$ABCD$ where

$bar{AD}$ ||

$bar{BC}$ and

$bar{AD} ~= bar{BC}$
Prove:

$bar{AB} " || " bar{CD}$

Parallelogram ABCD v3

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. bar{AD} " \|\| " bar{BC}$	$1. "Given"$
$2. ang CBD ~= ang ADB$	$2. "Alternate interior angles are congruent"$
$3. bar{BC} ~= bar{AD}$	$3. "Given"$
$4. bar{BD} ~= bar{BD}$	$4. ""$
$5. Delta ABD ~= Delta CDB$	$5. "Side-Angle-Side Postulate"$
$6. ang ABD ~= ang CDB$	$6. "Corresponding angles of congruent triangles are congruent"$
$7. bar{AB} " \|\| " bar{CD}$	$7. "If two lines are cut by a transversal, and alternate interior"$ $\ \ \ \ \ " angles are congruent, the lines are parallel"$