Question

1)
ABCD is a trapezium
AB 11 DC, P and Q are
midpoint of AD and BC
respectively then find the
length of PQ. If AB = 7cm
and DC = 17cm.​

Answer 1

Step-by-step explanation:

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=21(RB)

But RB=RA+AB

              =CD+AB              (∴   AR=CD by CPCTC)

∴   PQ=21(CD+AB)

                                        Hence proved.