Question

in the diagram above, △abc ≅ △bad. if ac = 8 m and ab = 17 m, how long is ad? (1 point) 15 m 17 m 19 m 20 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: Use Pythagorean theorem in $\triangle ABC$

In right - triangle $\triangle ABC$ with $\angle C = 90^{\circ}$, by the Pythagorean theorem $BC=\sqrt{AB^{2}-AC^{2}}$. 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.

Step3: Find length of $AD$

Since $\triangle ABC\cong\triangle BAD$, $AD = BC$. So $AD=15$ m.

Answer:

15 m