Practice Test on Parallelogram will help you to test your knowledge. Answer on your own for every question given below. Before you take the practice test, make sure you have read the concept completely and solved all problems. It becomes easy if you have a perfect grip on the entire concept. Also, it will avoid you to confuse while choosing the answers. Complete concept and Objective Questions on Parallelogram are given on our website for free of cost.
Tick (✔) the correct answer in each of the following
1. From the given options, which parallelogram two diagonals are not necessarily equal ………………..
(c) isosceles trapezium
Explanation: rhombus two diagonals are not necessarily equal.
2. A rhombus has diagonals of 16 cm and 12 cm. Find the length of each side?
Given that One diagonal is 16 and another 12 then half of both is 8 and 6. Diagonal of a rhombus bisect at 90º.
By pythogaurus theorem
h² = 8² + 6²
h² = 64 + 36=100
h = √100 = 10
Side = 10
3. Two adjacent angles of a parallelogram are (4b + 15)° and (2b – 10)°. The value of b is ………………. .
Explanation: sum of the adjacent angles of parallelogram=180
4b + 15 + 2b – 10=180
6b + 5 = 180
6b =180 – 5
6b = 175
b = 175/6
b = 29.16
4. From the given options, which parallelogram two diagonals do not necessarily intersect at right angles ………………..
Explanation: The diagonals do not necessarily intersect at right angles in a parallelogram.
5. The length and breadth of a rectangle are in the ratio 8 : 6. If the diagonal measures 50 cm. Find the perimeter of a rectangle?
(a) 800 cm
(b) 700 cm
(c) 600 cm
(d) 560 cm
(b) 700 cm
Explanation: Let m be the common multiple.
Length = 8m
Breadth = 6m
According to Pythagoras theorem,
(8m)² + (6m)²=(50)²
64m²+ 36m² = 2500
100m² = 2500
m² = 2500/100
m = 25
So, Length = 8m = 200 cm
Breadth = 6m = 150 cm
Perimeter = 2 (l × b)
= 2 (200 + 150)
= 700 cm
So, perimeter of rectangle is 700 cm.
6. The bisectors of any two adjacent angles of a parallelogram intersect at ………………..
Explanation: The bisectors of any two adjacent angles of a parallelogram intersect at 90°.
7. If an angle of a parallelogram is 2/3 of its adjacent angle find the angle of a parallelogram.
Explanation: Let m and n be the adjacent angles of a parallelogram.
Now, as we know that adjacent angles of a parallelogram are supplementary
Therefore, the sum of angles a and b will be 180º.
m + n = 180º
One angle is 2/3rd of the other.
m = 2/3 . n
2/3 . n + n = 180º
5/3 . n = 180º
n = 108º
m = 2/3 . 108º = 72º
8. The diagonals do not necessarily bisect the interior angles at the vertices in a ………………..
(d) all of these
Explanation: The diagonals do not necessarily bisect the interior angles at the vertices in a rectangle.
9. In a square PQRS, PQ = (3a + 5) cm and RS = (2a – 2) cm. Find the value of a?
Explanation: We know all the sides of a square are equal.
3a + 5 = (2a – 2)
3a – 2a = 5 + 2
a = 7
10. If one angle if a parallelogram is 24º less than twice the smallest angle then the largest angle if parallelogram is?
Explanation: Let the smallest angle be a then, the largest angle will be =180−a
but, the same equals to [2a − 24]
so we have [2a − 24] = 180 − a
3a = 204
a = 68
Thus, the largest angle 180 − 68 = 112 degree