Question

In the figure, AR=RC and PC is parallel to BQ. Name a triangle equal to triangle PCQ and a triangle equal in area to triangle APR, giving your reason. Hence prove that the areas of triangle APR and quadrilateral PBCR are equal.

Answer 1

Proved below.

Step-by-step explanation:

Given:

AR = RC and also PC║BQ.

ΔPCQ and Δ PBC are between same parallels PC and BQ and on same base

∴ ar (PCQ) = ar (PBC)

R is the midpoint of AC.

So PR is the median.

We know that a median divides a triangle into two equal halves.

∴ ar APR = ar PRC

Now Δ PRC is part of quadrilateral PBCR.

So therefore area of Δ APR cannot be equal to quadrilateral PBCR.