Question

use the image to answer the question. the perimeter of △abc is 20 cm. side de = 10 cm, and side fe = 3 cm. how long is side ac? (1 point)

Explanation:

Step1: Identify congruent triangles

By the markings (equal - angle marks and equal - side marks), $\triangle ABC\cong\triangle DEF$ (by Angle - Side - Angle or Side - Angle - Side congruence criteria).

Step2: Match corresponding sides

Since $\triangle ABC\cong\triangle DEF$, $AC = DF$ and $BC=FE$, $AB = DE$.

Step3: Use perimeter formula

The perimeter of $\triangle ABC=AB + BC+AC=20$ cm. We know $AB = DE = 10$ cm and $BC = FE=3$ cm.
Substitute the known values into the perimeter formula: $10 + 3+AC=20$.

Step4: Solve for $AC$

$AC=20-(10 + 3)$.
$AC=20 - 13$.
$AC = 7$ cm.

Answer:

7 cm