Question

Prove that the straight lines joining the
mid-points of the opposite sides of a
parallelogram are paralled to the other
pairs of Paralled side.​

Answer 1

Answer:

Step-by-step explanation:

Parallel lines are two lines in a plane that will never intersect (meaning they will continue on forever without ever touching).[1] A key feature of parallel lines is that they have identical slopes.[2] The slope of a line is defined as the rise (change in Y coordinates) over the run (change in X coordinates) of a line, in other words how steep the line is.[3] Parallel lines are most commonly represented by two vertical lines (ll). For example, ABllCD indicates that line AB is parallel to CD.

Answer 2

Let we have a parallelogram ABCD , and E and F are mid points of AB and CD respectively . We form our diagram , As :

Here Diagonals AC and BD and EF intersect at " O " .

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student-nameYash Khandelwal asked in Math

Prove that the straight lines joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides.

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student-nameAshutosh Verma answered this

in Math, Class

Answer :

Let we have a parallelogram ABCD , and E and F are mid points of AB and CD respectively . We form our diagram , As :

Here Diagonals AC and BD and EF intersect at " O " .

We know diagonals of parallelogram bisect each other , So

AO = CO

In ∆ ABC , we have

AE = BE , as we assumed E is mid point of AB

And

AO = CO , from property of parallelogram .

SO,

From conserve of mid point theorem , we get

EO | | BC , SO

EF | | BC ( As EO is part of line EF )

And

We know BC | | DA , from property of parallelogram , So

We can say

BC | | DA | | EF

So,

Joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides. ( Hence proved )