Use the image to answer the question.
An illustration shows a larger triangle upper A upper B upper C and a smaller triangle upper D upper E upper F, with labeled sides. On the first triangle, side upper B upper C is the base labeled as 36, side upper A upper B is the hypotenuse labeled as x, and vertical side upper A upper C is on the left and is not labeled. On the second triangle, side upper E upper F is the base labeled as 3, side upper D upper E is the hypotenuse labeled as 6, and vertical side upper D upper F is on the left and is not labeled.
If ΔABC is similar to ΔDEF , and BC= 36, EF= 3, and DE= 6, what is the measure of AB ?
Since ΔABC is similar to ΔDEF, the ratio of corresponding sides will be equal.
The ratio of the bases is BC/EF = 36/3 = 12.
Therefore, the ratio of the hypotenuses will also be 12, which means DE/AB = 6/AB = 12.
Solving for AB, we get AB = 6/12 = 1/2.
Therefore, the measure of AB is 1/2.