Question

TW is the mid segment of the trapezoid RSUV. If UV equals - Z +15, TW = -4z + 55, and RS = -3z + 43 what is the value of Z?

Answer 1

13

Explanation:

A trapezoid is a quadrilateral (has four sides and four angles) with two parallel opposite sides. These parallel sides are known as the bases.

According to the mid segment theorem of a trapezoid, The mid segment of a trapezoid is half the lengths of the two parallel sides.

Given that TW is the mid segment, UV and RS are the parallel bases, hence:

`TW=(UV+RS)/(2) \\\\-4z+55=((-z+15)+(-3z+43))/(2) \\\\-4z+55=(-4z+58)/(2) \\\\-8z+110=-4z+58\\\\-4z+8z=110-58\\\\4z=52\\\\z=13`