\n ![\"The](\"/api/assets/47494a8eebb807a036fdcfe6a7273283e1cc6c655d4cffbd5462cb3daed5ee37\")
\n In above, what is the length of
?
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.
4
\n","ord":0},{"label":"B","content_html":"6
\n","ord":1},{"label":"C","content_html":"