Question

show that the line segment joining the point (4,2 and ( -6 ,4) and (-10,5) ,and (8, 1) bisect each other.

Answer 1

Please look the attachments below for answers.

Answer 2

Step-by-step explanation:

MATHS

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

question

December 20, 2019avatar

Manpreet Patwari

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ANSWER

In △ADC,S is the mid-point of AD and R is the mid-point of CD

In △ABC,P is the mid-point of AB and Q is the mid-point of BC

Line segments joining the mid-points of two sides of a triangle is parallel to the third side and is half of of it.

∴SR∥AC and SR=

2

1

AC ....(1)

∴PQ∥AC and PQ=

2

1

AC ....(2)

From (1) and (2)

⇒PQ=SR and PQ∥SR

So,In PQRS,

one pair of opposite sides is parallel and equal.

Hence, PQRS is a parallelogram.

PR and SQ are diagonals of parallelogram PQRS

So,OP=OR and OQ=OS since diagonals of a parallelogram bisect each other.

Hence proved.