Q. 185.0( 2 Votes )

D is the midpoint of side BC of triangle ABC; P and Q lie on sides BC and BA in such a way that triangle BPQ = ΔABC. Let’s prove that, DQ || PA.

Answer :

Given.


D is the midpoint of side BC of triangle ABC; P and Q lie on sides BC and BA in such a way that triangle BPQ = ΔABC


Formula used.


If 2 triangles are on same base And having equal area then they lies between 2 parallel lines.


Median divides triangle in 2 equal parts



As D is mid-point of side BC


AD is median


Triangle ADC = triangle ADB = × triangle ABC


As we have given with


Triangle BPQ = triangle ABC


Triangle BPQ = triangle ADB


Triangle BPQ = triangle BQD + triangle DQP


Triangle ADB = triangle BQD + triangle DQA


By subtracting triangle BQD from both sides


triangle DQP = triangle DQA


As both triangles triangle DQP , triangle DQA are equal


And both lies on same base DQ


Hence both triangle ’s lies between parallel lines DQ and PA


DQ || PA


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