Everything Maths Grade 10

Investigation: Proving a quadrilateral is a parallelogram

1.Prove that if both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallel-

ogram.

2.Prove that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

3.Prove that if one pair of opposite sides of a quadrilateral are both equal and parallel, then the quadrilateral

is a parallelogram.

A quadrilateral is a parallelogram if:

• Both pairs of opposite sides are parallel.


• Both pairs of opposite sides are equal.


• Both pairs of opposite angles are equal.


• The diagonals bisect each other.


• One pair of opposite sides are both equal and parallel.
  Exercise 7 – 3:

1.P QRSis a parallelogram.P S=OSandQO=QR.SOR^ = 96◦andQOR^ =x.

P S

Q R

O

a)Find with reasons, two other angles equal tox.

b)WriteP^in terms ofx.

c)Calculate the value ofx.

2.Prove that the diagonals of parallelogramM N RSbisect one another atP.

S R

䴀 N

倀

Hint: Use congruency.

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254 7.3. Quadrilaterals