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Type: Multiple-Choice
Category: Circles
Level: Grade 10
Author: nsharp1
Last Modified: 4 years ago

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Grade 10 Circles

What are the missing reasons in steps 2 and 6 for the proof?

Given the circle shown, where

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

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

$triangle EBD ~= triangle DCE$ .

Circle with Two Secants ABCDE

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