Question

q
Point upper A is in the lower left and point upper B is in the lower right. They are joined by a horizontal
baseline. Point upper C is plotted upward and slightly to the right from upper A. Point upper D is plotted upward and slightly to the left of upper B. Upper C and upper D are on the same horizontal value but are not connected by a line. An upward and rightward diagonal line connects vertex upper A with upper C on the left side. Another diagonal line joins vertex upper C with vertex upper B, and a right angle symbol is drawn at upper C. An upward and leftward diagonal line connects upper B and upper D on the right side. A right angle symbol is drawn at upper D. Another diagonal line connects upper D upper A, intersecting line upper C upper B and forming three triangles.


In the diagram above, △ABC ≅△BAD
. If AC=8 m
and AB=17 m
, how long is AD¯¯¯¯¯¯¯¯
?

(1 point)
Responses

19 m
19 m

15 m
15 m

20 m
20 m

17 m

Answer 1

Since △ABC ≅ △BAD, the vertices correspond A↦B, B↦A, C↦D. So BC corresponds to AD. In right triangle ABC (right angle at C) with hypotenuse AB = 17 and leg AC = 8,

BC = sqrt(AB^2 − AC^2) = sqrt(17^2 − 8^2) = sqrt(289 − 64) = sqrt(225) = 15.

Thus AD = 15 m.