Question

use the image to answer the question. in the diagram above, △abc ≅ △bad. if ac = 8 m and ab = 17 m, how long is ad? (1 point) 20 m 19 m 15 m 17 m

Explanation:

Step1: Recall congruent - triangle property

If $\triangle ABC\cong\triangle BAD$, then corresponding sides are equal. Side $AC$ in $\triangle ABC$ corresponds to side $BD$ in $\triangle BAD$, and side $BC$ in $\triangle ABC$ corresponds to side $AD$ in $\triangle BAD$. Also, in right - triangle $ABC$, we can use the Pythagorean theorem.
In right - triangle $ABC$ with $\angle C = 90^{\circ}$, by the Pythagorean theorem $BC=\sqrt{AB^{2}-AC^{2}}$.

Step2: Substitute the given values

Given $AC = 8$ m and $AB = 17$ m. Then $BC=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$ m.
Since $\triangle ABC\cong\triangle BAD$, $AD = BC$. So $AD = 15$ m.

Answer:

15 m