Math, asked by brokenwings085, 1 year ago

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

Answers

Answered by Shaizakincsem
24

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.

Answered by parthtoshatwad
9

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

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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


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