Question

use the image to answer the question. in the diagram above, $\triangle abccong\triangle bad$. if $ac = 8$ m and $ab = 17$ m, how long is $overline{ad}$? (1 point) 15 m 19 m 20 m 17 m

Explanation:

Step1: Recall property of congruent triangles

Corresponding sides of congruent triangles are equal. Since $\triangle ABC\cong\triangle BAD$, side $AC$ corresponds to side $BD$ and side $BC$ corresponds to side $AD$, and side $AB$ corresponds to side $BA$.

Step2: Identify the relevant corresponding - sides

We know that $AC = 8$ m and $AB = 17$ m. We want to find $AD$. In right - triangle $ABC$, using the Pythagorean theorem $BC=\sqrt{AB^{2}-AC^{2}}$. And since $\triangle ABC\cong\triangle BAD$, $AD = BC$.

Step3: Apply the Pythagorean theorem

$BC=\sqrt{AB^{2}-AC^{2}}=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$ m. Since $AD = BC$, $AD = 15$ m.

Answer:

15 m