Q5 of 24 Page 21

In the quadrilateral ABCD shown below, the sides AB and CD are parallel. M is the midpoint of the side BC.


The lines DM and AB extended, meet at N.


Are the areas of Δ DCM and Δ BMN equal? Why?

Given-

AB ∥ CD


BM = MC


In Δ DCM and Δ BMN,


∠DMC = ∠BMN (vertically opposite angles)


BM = MC


∠DCM = ∠MBN (alternate angle test, DC ∥ BN with BC as transversal).


Using the property,


If one side of a triangle and angle at its ends are equal to one side of another triangle and the angles at its ends, then the third angles are also equal and the sides opposite equal angle are equal.


∴ ∠CDM = ∠MNB


DM = MN


DC = BN


As all 3 sides and angles are equal.


Δ DCM ≅ Δ NBM


Also, congruent triangles have equal areas.


∴ area(Δ DCM) = area(BMN) …(eq)1


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In the quadrilateral ABCD shown below, the sides AB and CD are parallel. M is the midpoint of the side BC.


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