Question

If the midpoints of the consecutive sides of a quadrilateral are joined then show by using vectors that they form a parallelogram

Answer 1

We have parallelogram ABCD with midpoints P,Q,R,S.

Draw diagonal DB

SP = SA+AP

=1/2DA +1/2AB = 1/2

|SP|=1/2|DB|

RQ=RC+CQ

=1/2DC +1/2CB = 12

RQ∥DB  and |RQ|=1/2|DB

SP∥RQ  and |SP|=|RQ|

if two sides of a quadrilateral are parallel and equal,  the quadrilateral is a parallelogram.

So, PQRS  is a parallelogram.

If there is any confusion please leave a comment below.

Answer 2

Answer:

Step-by-step explanation:

Secondary SchoolMath 5+3 pts

If the midpoints of the consecutive sides of a quadrilateral are joined then show by using vectors that they form a parallelogram

Report by Brokenwings085 12.10.2018

Answers

parthtoshatwad

Parthtoshatwad · Helping Hand

Know the answer? Add it here!

Shaizakincsem

Shaizakincsem Samaritan

We have parallelogram ABCD with midpoints P,Q,R,S.

Draw diagonal DB

SP = SA+AP

=1/2DA +1/2AB = 1/2

|SP|=1/2|DB|

RQ=RC+CQ

=1/2DC +1/2CB = 12

RQ∥DB and |RQ|=1/2|DB

SP∥RQ and |SP|=|RQ|

if two sides of a quadrilateral are parallel and equal, the quadrilateral is a parallelogram.

So, PQRS is a parallelogram.

If there is any confusion please leave a comment below