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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

For the proof shown, choose the correct reasons for steps 4 and 6.

Given: The circle pictured with diameter

$bar{AD}$ (not drawn), with

$bar{AB}$ tangent to the circle, and line

$bar{AC}$ also not drawn.
Prove:

$triangle ABD \ ~ triangle CAD$ .

Circle with Secant CD and Tangent AB

$" Statement "$	$" Reason "$
$1. "Draw " bar(AD) \ & \ bar{AC}$	$1. "Two points create a line"$
$2. bar(AD) \ \ "is a diameter"$	$2. "Given"$
$3. ang ACD \ \ "is a right angle"$	$3. "Inscribed angle subtended by a diameter is a right angle"$
$4. bar(AB) \ \ "is tangent to the circle"$	$4.$
$5. bar{AB} _\|_ bar{AD}$	$5. "A tangent line is perpendicular to the diameter"$
$6. ang BAD \ \ "is a right angle"$	$6.$
$7. ang ACD ~= ang BAD$	$7. "All right angles are congruent"$
$8. ang ADC ~= ang ADB$	$8. "Reflexive property"$
$9. triangle ABD \ ~ triangle CAD$	$9. "AA"$