# 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.

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

Triangle ADC = triangle ADB = × triangle ABC

As we have given with

Triangle BPQ = triangle ABC

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Master Theorems in Circles42 mins  Quiz | Area and Parallelogram46 mins  Champ Quiz | Area of Triangle53 mins  Quiz | Surface Area & Volumes49 mins  Surface Area of Right Circular Cylinder52 mins  Quiz | Mensuration42 mins  NCERT | Imp. Qs. on Area of Parallelogram and Triangles43 mins  Proof of Important Theorems of Circles45 mins  NCERT | Imp Qs on Area of Parallelogram And Triangles44 mins  Champ Quiz | Area of Parallelogram55 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 