Question

In triangle ABC, AP and BQ are the medians. If AC= BC, show that the medians AP and BQ are equal, prove that AP= BQ
PLS ANSWER FAST

Answer 1

Answer:

To Prove :-

RA=1/3 AC

Construction :-

    Draw PS parallel to BR to meet AC at S.

Proof :-

In Δ BCR, P is the mid-point of BC and PS is parallel to BR.

Where, S is the mid-point of CR

So,   CS=SR (1)

Again, In Δ APS, Q is the mid-point of AP and QR  is parallel to PS.

Where, R is the mid-point of AS.

So,    ----- (2)

From equations (1) and (2),

We get, AR = RS = SC

⇒ AC=AR+RS+SC

⇒ AC=AR+AR+AR

⇒ AC=3AR

∴ AR=1/2AC

--Please refer to the attached image for clarification of diagram and points--