Question

7. In the figure, PQRS
is a parallelogram in
which point A is the
midpoint of side SR.
B is a point on
diagonal PR such that
RB =1\4PR . AB when produced meets RQ at C.q
Prove that point C is the midpoint of side QR
​

Answer 1

Answer:

Step-by-step explanation:

Let intersection of QS and RP be called O.

Since QS and RP are diagonals of the parallelogram PQRS,

QS bisects RP, or OR=OP=1/2 RP

It is given that RB=1/4 RP, or

                        RB=1/2 (1/2 RP)=1/2 OR

So, B is the midpoint of OR.

Using Mid Point Theorem,

AB is parallel to OS.

Now, AB extended produces BC, and OS extended produces OQ.

So, BC is parallel to OQ.

Also B is midpoint of OR.

So, in ΔROQ, since BC is parallel to OQ and B is midpoint of OR, using the converse of midpoint theorem,

         C is the midpoint of RQ.

Hence Proved

<Hope it helps :D>

Answer 2

Step -by-step explanation:

Let intersection of QS and RP be called O.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RP

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 OR

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.So, BC is parallel to OQ.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.So, BC is parallel to OQ.Also B is midpoint of OR.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.So, BC is parallel to OQ.Also B is midpoint of OR.So, in AROQ, since BC is parallel to OQ and B is midpoint of OR, using the converse of midpoint theorem,

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.So, BC is parallel to OQ.Also B is midpoint of OR.So, in AROQ, since BC is parallel to OQ and B is midpoint of OR, using the converse of midpoint theorem,C is the midpoint of RQ.

Let intersection of QS and RP be called O.Since QS and RP are diagonals of the parallelogram PQRS,QS bisects RP, or OR-OP-1/2 RPIt is given that RB=1/4 RP, or RB-1/2 (1/2 RP)=1/2 ORSo, B is the midpoint of OR.Using Mid Point Theorem,AB is parallel to OS.Now, AB extended produces BC, and OS extended produces OQ.So, BC is parallel to OQ.Also B is midpoint of OR.So, in AROQ, since BC is parallel to OQ and B is midpoint of OR, using the converse of midpoint theorem,C is the midpoint of RQ.Hence Proved