Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 4 Practical Geometry Questions Solution. In this chapter, there is total 20 math problems. We have given each questions solution step by step.
1.) What is the minimum number of measurements required to construct a parallelogram?
ANSWER:
Minimum number of measurements required to construct a parallelogram is 3.
2.) How many elements are required for constructing a quadrilateral uniquely?
ANSWER:
5 elements are required for constructing a quadrilateral uniquely.
3.) In the figure given below AB= = , name the angles which are equal.
ANSWER:
Given that,
AB= =
The angles which are equal are,
∠∠
∠A∠C
4.) If the diagonals of a quadrilateral bisect each other at right angles, then which type of a quadrilateral is it?
ANSWER:
We know,
The diagonals of a quadrilateral bisect each other at right angles, thentype of a quadrilateral is Rhombus or square.
5.) In the given figure, PQRS is a parallelogram if ∠ =90o, then what will be the name of the quadrilateral?
ANSWER:
In the given figure, PQRS is a parallelogram if ∠ =90o
Also, opposite sides are equal.
I.E. PS = QR and PQ = SR
The Type of Quadrilateral is Rectangle.
6.) At least how many measurements are required to construct a square?
ANSWER:
To construct a square at leastOne side or one diagonal is required.
7.) ABCD is a rhombus. If OD=4cm and AO=3cm, then find the value of AC+BD.
ANSWER:
Given that,
ABCD is a rhombus.
OD=4cm and AO=3cm
We have to find the value of AC+BD.
We know,
The diagonals of a rhombus bisect each other at right angle.
BD = 2 x OD
BD = 2 x 4
BD = 8 cm.
Now,
AC = 2 x OA
AC = 2 x 3
AC = 6 cm.
The value of AC+BD = 8 + 6 = 14 cm.
8.) At least how many measurements are required for constructing rhombus?
ANSWER:
For constructing rhombus at least2 (one side and one diagonal)are required.
9.) Name the property which is used to construct a parallelogram if it’s one side and both diagonals are given.
ANSWER:
If one side and both diagonals are given to construct a parallelogram,
We use the property which is,
The diagonals of a parallelogram bisect each other.
10.) Name the property which is used to construct a rhombus, if it’s both diagonals are given.
ANSWER:
If it’s both diagonals are givento construct a rhombus,
We use the property which is,
The diagonals of a rhombus bisect each other at right angle.
11.) In the given figure KITE is a parallelogram then find KE+ET
ANSWER:
Given that,
KITE is a parallelogram.
We have to find KE+ET.
We know,
A parallelogram is a quadrilateral whose opposite sides are parallel and equal.
Side KI = Side TE
Side KI = 4.2 cm
Side TE = 4.2 cm
Now, Side IT = Side KE
Side IT = 3.8 cm.
Side KE= 3.8 cm.
KE+ET = 4.2 cm + 3.8 cm.
KE+ET = 8 cm.
12.) Two sticks each of length 5cm are crossing each other such that they bisect each at right angles. What shape is formed by joining their end points?
ANSWER:
Given that,
Two sticks each of length 5cmare crossing each other such that they bisect each at right angles.
The shape is formed by joining their end points is square.
13.) CARE is a rhombus whose diagonals intersect at O. If AR=10cm and diagonal AE=16cm then find the length of CR.
ANSWER:
Given that,
CARE is a rhombus whose diagonals intersect at O.
AR=10cm and diagonal AE=16cm
We have to find the length of CR.
We know the property of Rhombus.
The diagonals of a rhombus bisect each other at right angle.
In Triangle ROA,
Angle O = 900
We use Right Angle triangle theorem,
AR2 = OA2 + OR2
OA = AE / 2 = 16 / 2 = 8 cm.
102 = 82+ OR2
OR2= 100 – 64
OR2= 36
OR= 6 cm
We have to find the length of CR
Length of CR = 2 x OR
Length of CR = 2 x 6
Length of CR = 12 cm.
14.) If the diagonals of a quadrilateral are of length 10cm and 12cm and they bisect each other at right angles then what is the length of each side of the quadrilateral?
ANSWER:
Given that,
The diagonals of a quadrilateral are of length 10cm and 12cm and they bisect each other at right angles.
Let, we draw rough figure.
In Triangle AOB,
Angle O = 900
OA = AC / 2
OA = 12 / 2
OA = 6 CM.
Also,
OB = BD / 2
OB = 10 / 2
OB = 5 cm.
We use Right Angle triangle theorem,
AB2 = OA2 + OB2
AB2 = 62 + 52
AB2 = 36 + 25
AB2 = 61
AB = √m
16.) Three angles of a quadrilateral are equal. If the measure of fourth angle is °, then find the measure of equal angles.
ANSWER:
Given that,
Three angles of a quadrilateral are equal.
Measure of fourth angle is °.
We know,
Sum of interior angle of a quadrilateral is 3600.
Let,
The same angle is x.
X + x + x + ° = 3600
3x = 3600 -°
3x = 2100
x = 210 / 3
x = 700
The measure of equal angles is 700
17.) From the given figure find x and y.
ANSWER:
We have to find x and y.
From fig,
Side ST = Side TF
We know,
Opposite angles of Equal sides are equal.
Angle x = Angle F = 1100
Now,
We know,
Sum of interior angle of a quadrilateral is 3600.
1100 + 1100 + 600 + y = 3600
y = 3600 – 2800
y = 800
Value of x and y are 1100and800 respectively.
18.) In the given parallelogram ABCD, ⊥, ⊥. If ∠ = °, then find ∠.
ANSWER:
Given that,
Parallelogram ABCD
⊥, ⊥.
∠ = °
We have to find ∠.
From figure,
In triangle CDE
∠ + ∠ + ∠ = 180°
400 + 900+ ∠ = 180°
∠ = 180° – 1300
∠ = 500
Now, opposite angle of parallelogram are equal.
∠ = ∠B = 500
Now,
In triangle BCF
∠BCF + ∠FB + ∠FBC = 180°
∠BCF + 900 +500 = 180°
∠BCF = 180° – 1400
∠BCF = 400
Sum of adjacent angles of parallelogram is 180°
∠B + ∠C = 180°
∠C = 180° – 500
∠C = 130°
Now,
∠C = ∠ + ∠BCF + ∠.
130° = 400+ 400+ ∠.
∠ = 130° – 80°
∠ =500
19.) PQRS is a rectangle in which diagonals intersect at J. Find the value of x if JR = (8x+4) units and PR = (24x- 8) units.
ANSWER:
Given that,
PQRS is a rectanglein which diagonals intersect at J.
JR = (8x+4) units and PR = (24x- 8) units
We know,
The diagonals of a rectangle are equal and bisect each other.
PR = PJ + JR
PR = 2 x JR
But,
PR = (24x- 8) units and JR = (8x+4) units
(24x- 8) units = 2 (8x+4) units
(24x- 8) units = 16x + 8
By rearranging,
24x- 16x = 8 + 8
8x = 16
X = 2
Value of X is 2.
20.) In the given figure, ABCD is a square. If = √. Find AB + BC.
ANSWER:
Given that,
ABCD is a square.
= √
We have to find AB + BC.
We know,
The diagonals of a square are equal and bisect each other at right angle.
= OD = √
We use Right angle triangle theorem,
CD2 = OC2 + OD2
CD2 = (√)2 + (√)2
CD2 = 8 + 8
CD2 = 16
CD = 4 cm.
We know,
All sides of square are equal.
AB = BC = CD = AD = 4 cm
Now, we find AB + BC
AB + BC = 4 + 4 = 8 cm.
Chapter 1 |
Rational Numbers |
Chapter 2 |
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Chapter 3 | |
Chapter 5 |