Question

Let ABCD be a rectangle with AB = 4 and BC = 1. Denote by M the midpoint of line segment AD and by P the leg of the perpendicular from B onto CM.

a) Find the lengths of P B and PM.

b) Find the area of ABPM.

c) Consider now ABCD being a parallelogram. Denote by M the midpoint of side AD and by P the leg of the perpendicular from B onto CM. Prove that AP = AB. Hint: Extend line MC and denote by S its intersection with line AB and observe that two congruent triangles are formed.

Answer 1

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