Segment AB is a midsegment of trapezoid WXYZ, and segment ZY is parallel to segment WX. Determine WX if AB = 10 cm and ZY = 7 cm. Justify your answer.
In the trapezoid xwzy,lk is the mid-segment. Find the length of zw.
To determine the length of segment WX, we need to use the properties of a midsegment of a trapezoid. In a trapezoid, a midsegment is a line segment that connects the midpoints of the two non-parallel sides.
First, let's label the midpoints of sides WZ and XY as M and N, respectively. The midsegment AB connects M and N. Since AB is a midsegment, it is parallel to the bases WZ and XY, and its length is equal to the average of the lengths of the bases.
Given that AB = 10 cm, we know that the average of the lengths of the bases is 10 cm. Since ZY = 7 cm, we can express the lengths of the bases as:
WX = 2(AB) - ZY
Substituting the given values:
WX = 2(10 cm) - 7 cm
Simplifying:
WX = 20 cm - 7 cm
WX = 13 cm
Therefore, the length of segment WX is 13 cm.