Question

consider the non - right triangle shown below, with vertices a, b, and c, and opposing sides of lengths a, b, and c. let point c (not shown) be the image of point c when the triangle is reflected across $overline{ab}$. which of the following is an expression for the perimeter of the resulting quadrilateral cbca? 2(c + a + b) 2(c + a) 2(a + b) 2(c + b) 2(a + b)+c

Explanation:

Step1: Recall reflection properties

When point $C$ is reflected across $\overline{AB}$ to get $C'$, we have $AC' = AC=b$ and $BC'=BC = a$.

Step2: Find perimeter of quadrilateral $C'BCA$

The perimeter $P$ of quadrilateral $C'BCA$ is $P=AC'+BC'+BC + AC$. Substituting $AC' = b$, $BC'=a$, $BC = a$ and $AC = b$, we get $P=b + a+a + b=2(a + b)$.

Answer:

$2(a + b)$