document.write( "Question 1102352: In △ABC, m∠CAB = 60° and point D ∈ BC so that AD = 10 in, and the distance from D to AB is 5in. Prove that AD is the angle bisector of ∠A. Which theorem used to solve this problem?
\n" ); document.write( "a) Leg opposite to 30°∠
\n" ); document.write( "b) Leg opposite to 30°∠ converse
\n" ); document.write( "c) Median to hypotenuse theorem
\n" ); document.write( "d) Median to hypotenuse theorem converse \n" ); document.write( "

Algebra.Com's Answer #717138 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The names of the theorems you show as the answer choices are not names that are used universally, or probably even widely. There is no median to a hypotenuse in this problem, so answer choices c and d are out. But whether the answer is a or b depends on how the theorems were presented to you in your book and/or by your teacher.

\n" ); document.write( "It is clear that AD bisects angle A; what the answer is to the problem only you can figure out.

\n" ); document.write( "It is given that angle A is a 60 degree angle.

\n" ); document.write( "We also know that AD is 10 and BD is 5; also, since BD is the distance from D to AB, we know BD is perpendicular to AB. That makes triangle ABD a 30-60-90 right triangle, with angle DAB 30 degrees.

\n" ); document.write( "Then since angle BAD is 30 degrees and angle A is 60 degrees, AD bisects angle A.

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