Question

Given: MNOK is a trapezoid, MN=OK, m∠M=60°, NK ⊥ MN , MK=16cm Find: The midsegment of MNOK

Answer 1

Answer:

12 cm

Step-by-step explanation:

1. Consider right triangle MNK. In this triangle angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with measure of 30°, then this leg is half of the hypotenuse, MN=8 cm.

2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.

3. Trapezoid MNOK is isosceles, because MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.

4. The midsegment of the trapezoid is

$\dfrac{MK+NO}{2}=\dfrac{16+8}{2}=12\ cm.$