Question

in the adjacent figure ab || pq || cd, q is the mid point of ac. if ab=4cm and cd=6cm then find pq.

Answer 1

ans-5cm.
..............

Answer 2

Answer:

Ans. = 5cm

Step-by-step explanation:

Join AP

Extend AP and CD, so that they intersect. Name that point  R

Now ,

Since PQ || CD and Q is the mid point of AC

Therefore, AP = PR

Also, PQ = 1/2 CR  ..(1)

Now in Triangles ABP and RPD

Angle BAP = Angle DRP  (Alternate interior angles of line CR || AB)

AP = PR (Proved above)

Angle APB = Angle RPD  (Vertically opposite angles)

Therefore Triangle ABP is Congruent to Triangle RPD by ASA rule.

SO, DR = AB =4cm (By CPCT)

We know that

CR = CD +DR

CR = CD + AB (DR = AB) ..(2)

From Eq. 1 and 2

PQ = 1/2(CD + AB)

PQ = 1/2(6+4)

PQ = 1/2(10)

PQ = 5 cm