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Type: Multiple-Choice
Category: Circles
Level: Grade 10
Author: nsharp1
Created: 7 years ago

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Circles Question

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Given the circle below, where

$m \stackrel{\frown}{EB} = m \stackrel{\frown}{DC}$ and with lines

$bar{EC}, bar{BD}, & \ bar{ED}$ not drawn, prove that

$triangle EBD ~= triangle DCE$ .

Circle with Two Secants ABCDE

$" Statement "$	$" Reason "$
$1. "Draw lines " bar{EC}, bar{DB}, & \ bar{ED}$	$1. "Two points define a line"$
$2.$	$2. "Given"$
$3. m ang EDB = 1/2 m \stackrel{\frown}{EB}$	$3.$
$4. m ang CED = 1/2 m \stackrel{\frown}{CD}$	$4. "Measure of inscribed angle is 1/2 the measure of intercepted arc"$
$5. 1/2 m \stackrel{\frown}{EB} = 1/2 m \stackrel{\frown}{DC}$	$5.$
$6.$	$6. "Substitution Property of Equality"$
$7. ang EDB ~= ang CED$	$7. "Definition of congruent angles"$
$8. ang EBD ~= ang ECD$	$8.$
$9. bar{ED} ~= bar{ED}$	$9. "Reflexive Property"$
$10. triangle EBD ~= triangle DCE$	$10.$

Grade 10 Circles

What is the missing reason in step 5?

Multiplicative Identity Property
Multiplicative Inverse Property
Multiplicative Property of Equality
Closure Property of Multiplication