Question

in the given figure ABC is trapezium, P is the midpoint of side AB and PR||AB||DC.
Prove that
1. R is the midpoint of side BC
2. Find the length of PR, if AB=12cm and DC=8 cm​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

•1)As P is the midpoint of side AB and PR||AB||DC

then R would be the midpoint of CB (as PR||AB||DC)

•2)According to the question

AB= 12 cm

DC= 8 cm

∆BDC & ∆ BQR

angle BDC = angle BQR

(as these are corresponding angles of parallel lines)

and so, ∆BDC≈∆BQR

thus,BD/QR= DC/QR

as Q is the middle point of BD

then, QR = 1/2 × DC

similarly QP = 1/2× AB

and now

QP+ QR = (1/2 × DC) +(1/2× AB )= 1/2 ×(AB+DC) = 1/2×(12+8) = 10 cm