Question 1102352
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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.<br>
It is clear that AD bisects angle A; what the answer is to the problem only you can figure out.<br>
It is given that angle A is a 60 degree angle.<br>
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.<br>
Then since angle BAD is 30 degrees and angle A is 60 degrees, AD bisects angle A.<br>