In triangle ABC, the medians CD and BE are produced to P and Q
respectively
such that CD = DP and BE = EQ. Prove that the points P, A, Q are collinear.
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Given : triangle ABC, the medians CD and BE are produced to P and Q respectively
CD = DP and BE = EQ
To Find : Prove that the points P, A, Q are collinear.
Solution:
medians CD produced to P
=> AD = BD
DP = CD given
in ΔADP and Δ BDC
AD = BD
∠ADP = ∠BDC ( vertically opposite angle)
DP = CD given
=> ΔADP ≅ Δ BDC
=> ∠DAP = ∠DBC
=> ∠BAP = ∠ABC
∠BAP = ∠ABC => PA || BC
Similarly we can show that
QA || BC
PA || BC
QA || BC
=> PA || QA
as A is common
Hence PA and QA are same line
Hence P , A & Q are collinear
QED
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