In above, what is the length of ?

Question

Accepted Answer

Choice B is correct. Triangles ADB and CDB are both triangles and share . Therefore, triangles ADB and CDB are congruent by the angle-side-angle postulate. Using the properties of triangles, the length of is half the length of hypotenuse . Since the triangles are congruent, . So the length of is . Alternate approach: Since angle CBD has a measure of , angle ABC must have a measure of . It follows that triangle ABC is equilateral, so side AC also has length 12. It also follows that the altitude BD is also a median, and therefore the length of AD is half of the length of AC , which is 6. Choice A is incorrect. If the length of were 4, then the length of would be 8. However, this is incorrect because is congruent to , which has a length of 12. Choices C and D are also incorrect. Following the same procedures as used to test choice A gives a length of for choice C and for choice D. However, these results cannot be true because is congruent to , which has a length of 12.

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