Question

in the given figure A , B , C are the mid points of PQ , QR and RP respectively . price that AQBC is a rectangle .​

Answer 1

Answer:

Between the triangle ARP and CRQ applying mid point theorem

RP ∥ BC and

RP =1/2BC = CQ.

And AR = RC ( R is the mid point of AC )

again PR ∥ BC and AC is the transversal.

Therefore angle ARP = angle RCQ.

Therefore the triangles are congruent by SAS test.

Area ΔARP=AreaΔ RCQ.

By applying the same midpoint theorem we can prove that each of the four triangles have the same area.

So, they divide the triangle into four equal areas.

Now total area = 20 sq. cm.

Therefore area of the Δ PQR is 20 sq.cm divided by 4 = 5 sq.cm