Question

In the figure below, the lines AB and CD are parallel and M is the mid point of AB.

(i) Compute the angle of ∆AMD, ∆MBC and ∆DCM?

(ii) What is special about the quadrilateral AMCD and MBCD?

Answer 1

Given AB = 12 cm and M is the mid-point of AB.

∴ AM = MB = 6 cm

In quadrilateral AMCD,

AM = CD

AB||CD ∴ AM||CD

∴ AMCD is a parallelogram.

∴ ∠AMD = ∠CDM (Alternate interior angles)

∠ADM = ∠CMD (Alternate interior angles)

∠A = ∠DCM = 40° = ∠CMB

∴ ∠MCB = 80° [180 – (60 + 40)]

(i) The angles of ∆AMD, ∆MBC and ∆DCM are 40°, 60° and 80° respectively.

(ii) Both of them are parallelograms.