Question

3. ABCD is a quadrilateral in which AB || CD. P is the midpoint of BC. PQ is drawn parallel to CD
which meets AD at Q. Prove that PQ bisects AD. Also, prove that PQ bisects both the diagonals,
AC and BD.​

Answer 1

Step-by-step explanation:

Given :

ABCD is a Quadrilateral in which AB || CD

P is mid point Of BC and PQ || CD is Drawn

which meet AD at Q

AC and BD are diagonal which intersects PQ at L

And M

Find :

PQ Bisect AC and BD at L and M

Solution :

ln ∆ ABC

P is midpoint Of BC

PQ || CD

CD || AB

Therefore L is Midpoint Of AC

Since AB || PQ

PQ || CD

CP = PB ( Since P midpoint BC )

Therefore DQ = QA

DM = MB

Hence Proved

PQ Bisect AC at L and BD at M

Some Important Properties Quadrilateral

In a Parallelogram Opposite Side are equal

A Diagonal Of a parallelogram divides it two congruent triangle

The diagonal of a parallelogram Bisect each other

If a Quadrilateral , each pair of opposite angle is equal then it is a parallelogram

If the diagonal of a Quadrilateral Bisect each other then it is a parallelogram

A Quadrilateral is a parallelogram if a pair of opposite side equal and parallel