Question

prove that the line joining the midpoints of any two sides of a triangle is parallel to the third side

Answer 1

Given :- In ∆ABC, P is midpoint on AB and Q is midpoint on AC.

To prove :- PQ || BC.

Proof :- In∆ ABC, P and Q are m.p of side AB and AC, respectively.

AP = PB and AQ = QC

AP/PB = AQ/QC = 1

:-Using converse theorem of Proportionality we get,

PQ || BC. ...........(proved)

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Answer 2

Solution _____________♥

●Given that ABC is a traingle and D and E are mid points of traingle. Construction : Join C and D , B and E. Prove that : DE // BC.Proof :  In ΔADE = ΔBDE AD = BD ( D is mid point)
 DE = DE ( same height) Area of ΔADE = Area of ΔBDE -------------(1)

 In ΔADE = ΔCDE AE = EC ( E is mid point) 
DE = DE ( same height) Area of ΔADE = Area of ΔCDE -------------(2)

_____from (1) and (2) ______
we get  Area of ΔBDE = Area of ΔCDE ∴ DE // BC.

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