Question

In trapezium ABCD, Seg AB || Seg DC. Points Pand Q are the midpoints of Seg AD and Seg BC respectively. If AB = 10cm, DC = 8cm then find the value of Seg PQ.​

Answer 1

Step-by-step explanation:

Given,

ABCD is a trapezium in which AB∥DC and P, Q are the midpoints of AD & BC respectively

Construction : Join CP and produce it to meet AB produced to R.

In ΔPDC & ΔPAR

PD=PA (∵ P is the midpoint of AD)

∠CPD=∠RPA (Vertically opposite angles)

∠PCD=∠PRA (alternate angle)

∴ ΔPDC≅ΔPAR using A as criterion

⇒CP=CR (CPCTC)

Also,

In ΔCRB,

P is the midpoint of CR (proved above)

Also, Q is the midpoint of BC

⇒ By midpoint theorem PQ∥AB and PQ=

2

1

(RB)

But RB=RA+AB

=CD+AB (∴ AR=CD by CPCTC)

∴ PQ=

2

1

(CD+AB)

Answer 2

Step-by-step explanation:

• THE ANSWER IS WRITTEN ABOVE

HOPE YOU WOULD LIKE