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Type: Multiple-Choice
Category: Quadrilaterals
Level: Grade 10
Standards: HSG-CO.C.11
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 8 of the following proof?

Given: Quadrilateral

$ABCD$ with diagonal

$bar{BD}$ where

$bar{AB}$ ||

$bar{CD}$ and

$bar{BC}$ ||

$bar{AD}$
Prove:

$ang BAD ~= ang DCB$

Parallelogram ABCD v3

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. bar{AB}$ \|\| $bar{CD}$	$1. "Given"$
$2. ang ABD ~= ang CDB$	$2. "Alternate interior angles are congruent"$
$3. bar{BC}$ \|\| $bar{AD}$	$3. "Given"$
$4. ang ADB ~= ang CBD$	$4. "Alternate interior angles are congruent"$
$5. m ang ABD = m ang CDB, \ \ m ang ADB = m ang CBD$	$5. "Definition congruent angles"$
$6. m ang ABD + m ang ADB + m ang BAD = 180°,$ $\ \ \ \ \ \ \ \ \ m ang CDB + m ang DCB + m ang CBD = 180°$	$6. "Sum of angles in a triangle is 180°"$
$7. m ang CDB + m ang DCB + m ang CBD =$ $\ \ \ \ \ \ \ \ \ \ m ang ABD + m ang ADB + m ang BAD$	$7. "Substitution Property of Equality"$
$8. m ang DCB = m ang BAD$	$8. ""$
$9. ang BAD ~=ang DCB$	$9. "Definition of congruent angles"$