In isosceles trapezoid HJKL, HJ ll LK. Suppose that points M,N,P, and Q are midpoints of the sides HL,HJ,JK, and LK. If the length of diagonal HK is 10 cm, find the perimeter of MNPQ.
We will use the following theorem:
Line segment which connects midpoints of two sides of a triangle is parallel to the third side and is half of the length of the third side.
Let's first look at triangle HJK, in it the line segment NP connects two of the triangles sides midpoints and since the third side of the triangle is HK=10cm it follows that NP=5cm.
Similarly from triangle HKL we get QM=5cm.
Since this is isosceles trapezoid it follows that both of its diagonals are equal i.e. HK=JL=10cm. Now from triangles HJL and JKL we get MN=5cm and PQ=5cm.
We can now calculate perimeter of MNPQ.