Question

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Q.1) Prove that in a parallelogram opposite angles are equal.

Q.2) Prove that in a parallelogram,diagonals bisect each other.

Q.3)Prove that a quadrilateral is a parallelogram iɴ it's opposite sides are equal.


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Nᴏ sᴘᴀᴍ✘

sᴘᴀᴍᴍᴇʀs sᴛᴀʏ ᴀᴡᴀʏ✘​

Answer 1

Answer:

A quadrilateral is a parallelogram if: its opposite angles are equal, or. its opposite sides are equal, or. one pair of opposite sides are equal and parallel, or.

Step-by-step explanation:

If the opposite sides of a quadrilateral are equal and parallel, then it is a parallelogram. If the opposite angles in a quadrilateral are equal, then it is a parallelogram. A parallelogram that has all equal sides is a rhombus.

Answer 2

Question 1:

Statement: In a parallelogram, opposite angles are equal.

Given : Parallelogram ABCD

To prove ; A = ZC and ZB = ZD

Proof:

In parallelogram ABCD, Consider,

AD II BC and AB is transversal

ZA + ZB = 180° [Co - int. Angles)...... (i)

Now, consider AB II DC and BC transversal

ZB + ZC = 180° [Co - int. Angles.. (ii)

From (i) and (ii) we get

ZA + ZB = ZB + ZC

ZA = ZC

ZB = ZD

Hence, it is proved.

Question 2:

ABCD is a parallelogram, diagonals AC and BD intersect at O

In triangles AOD and COB,

DAO = BCO(alternate interior angles)

AD = CB(alternate interior angles)

Z ADO = Z CBO(ASA)

AOD = COB

Hence, AO = CO and OD = OB (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other.

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