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