Question

Medians CM and BN of AABC are produced
to P and respectively such that CM = MP
and BN = NQ. Prove that the points P, A, Q
are callinear and PA = AQ
N
B
C
pa and
[Hint: Join MN, MN = -PA and Il to PA
2.
1
in ACAP MN = AQ and Il to AQ in
ABAQ etc.)​

Answer 1

Step-by-step explanation:

Correct option is

A

1

Given: BP and CQ are medians of AB and AC respectively of triangle ABC

BP and CQ are produced to M and N such that BP = PM and CQ = QN

In △APM and △BPC,

AP=PC

PM=BP

∠APM=∠BPC ...(Vertically opposite angles)

therefore, △APM≅△BPC ...(SAS rule)

∠AMP=∠PBC ...(By cpct)

Similarly, △AQN≅△BPC

hence, ∠ANQ=∠QBC ..(By cpct)

Hence, N, A, M lie on a straight line.

NM=NA+AM=BC+BC=2BC

hence, A is the mid point of MN

solution