In the figure below, the lines AB and CD are parallel and M is the mi

1.	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» 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.

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»

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.