Question

extra practice trapezoids and kites example 1 1. lamp shade the lamp - shade shown is a trapezoidal prism. the front face of the lamp is an isosceles trapezoid. kl = 2x + 2, mj = 6x + 2, lm = 5x - 5, and kj = 3x - 1. a. prove x = 3.

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, the non - parallel sides are equal. So, $LM = KJ$.
$5x - 5=3x + 1$

Step2: Solve the equation for x

Subtract $3x$ from both sides: $5x-3x - 5=3x-3x + 1$, which simplifies to $2x-5 = 1$.
Then add 5 to both sides: $2x-5 + 5=1 + 5$, getting $2x=6$.
Divide both sides by 2: $\frac{2x}{2}=\frac{6}{2}$, so $x = 3$.

Answer:

$x = 3$ is proven as shown above.