Definition of parallelogram :
A parallelogram is a quadrilateral which has opposite sides parallel.
Properties of parallelogram :
Problem 1 :
For the parallelogram given below, solve for m and n.
Solution :
Since the given shape is a parallelogram, the diagonals will bisect each other.
AO = OC m + 8 = 3m ---(1) 8 = 3m - m 2m = 8 m = 4 |
BO = OD 9 = 2n - 1 2n = 9 + 1 2n = 10 n = 5 |
Problem 2 :
For the parallelogram given below, solve for j and k.
Solution :
AO = CO k + 10 = 6k 6k - k = 10 5k = 10 k = 2 |
BO = OD 5j - 9 = 3j 5j - 3j = 9 2j = 9 j = 4.5 |
Problem 3 :
In parallelogram PQRS, solve for x and y.
Solution :
QT = ST 2x + 8 = 18 2x = 18 - 8 2x = 10 x = 10/2 x = 5 |
PT = TR 4y - 2 = 22 4y = 22 + 2 4y = 24 y = 24/4 y = 6 |
Problem 4 :
Solve the n in the following parallelogram ABCD. Find length of the diagonal BD.
Solution :
Diagonals will bisect each other.
3n - 6 = 5n - 122
3n - 5n = -122 + 6
-2n = -116
Dividing by 2 on both sides.
n = 116/2
n = 58
Length of BD = 3n - 6 + 5n - 122
= 8n - 128
= 8(58) - 128
= 464 - 128
= 336
So, length of the diagonal BD is 336.
Problem 5 :
Length of the longer diagonal in the parallelogram FAST.
Solution :
FO = 5.5, then FS = 5.5(2) ==> 11
TO = 3x - 1, OA = 2x + 7
3x - 1 = 2x + 7
3x - 2x = 7 + 1
x = 8
Length of diagonal TA = 3x - 1 + 2x + 7
= 5x + 6
= 5(8) + 6
= 40 + 6
= 46
So, length of the longer diagonal is 46.
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