Question

In parallelogram (EFGH,) let (M) be the midpoint of side (EF,) and let (N) be the midpoint of side (EH.) Line segments (FH) and (GM) intersect at (P,) and line segments (FH) and (GN) intersect at (Q.) Find (PQ/FH.)

a) (1/4)
b) (1/2)
c) (3/4)
d) (1)

Answer 1

To find PQ/FH, we use similar triangles and ratios to determine that PQ/FH is equal to 1/2.

Step-by-step explanation:

To find PQ/FH, we need to determine the lengths of PQ and FH.

From the given information, we know that M is the midpoint of EF and N is the midpoint of EH. Therefore, MF is equal to half of EF and NH is equal to half of EH.

Since GM intersects FH at P and GN intersects FH at Q, we can conclude that angle PFQ is equal to angle MFP and angle QFP is equal to angle NFP.

By using similar triangles and ratios, we find that PQ/FH is equal to 1/2. Therefore, the correct answer is (b) 1/2.