Sail E0 Webinar

8th Grade > Mathematics

UNDERSTANDING QUADRILATERALS MCQs

Total Questions : 464 | Page 3 of 47 pages
Question 21.
Every rhombus is a trapezium.
 Discuss Question

:
False
Atrapeziumis a quadrilateral with exactly one pair of parallel sides.
A rhombusis a parallelogram having all sides equal.
Question 22.
The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45∘. Find the angles of the parallelogram.
 Discuss Question

:
Let ABCD be a parallelogram, where BE and BF are the perpendicular through the vertex B to the sides DC and AD, respectively.
The Angle Between The Two Altitudes Of A Parallelogram Throu...
Let ∠A=∠C=x,∠B=∠D=y [∵ opposite angles are equal in parallelogram]
Now, ∠A+∠B=180∘ [∵ adjacent sides of a parallelogram are supplementary]
⇒x+∠ABF+∠FBE+∠EBC=180∘
⇒x+90∘−x+45∘+90∘−x=180∘
[∵InΔABF,∠ABF=90∘−xandinΔBEC,∠EBC=90∘−x]
⇒−x=180∘−225∘⇒x=45∘∴∠A=∠C=45∘∠B=45∘+45∘+45∘=135∘⇒∠D=135∘
Hence the angles are 45∘,135∘,45∘,135∘.
Question 23.
In parallelogram PQRS, O is the mid-point of SQ. Find ∠S,∠R, PQ, QR and diagonal PR.
In Parallelogram PQRS, O Is The Mid-point Of SQ. Find ∠S,â...
 Discuss Question

:
Given, ∠RQY=60∘
∠SRQ=∠RQY [SR∥PY, RQ is the transversal]
⇒∠R=60∘
∴∠S=180∘−∠R=180∘−60∘=120∘ [∵ adjacent angles are supplementary]
Also, SR = 15 cm
⇒ PQ = 15 cm [∵ opposite sides of a parallelogram are equal]
And PS = 11 cm
⇒ QR = 11 cm [∵ opposite sides of a parallelogram are equal]
PR is bisected by SQ, so PR=2×PO=2×6=12cm
Question 24.
The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
 Discuss Question

:
Given, AC = 15 cm, BD = 8 cm.
The Diagonals Of A Rhombus Are 8 Cm And 15 Cm. Find Its Side...
Since, the diagonals of a rhombus bisect each other at 90∘, therefore in the ΔAOB, we have
AB2=OA2+OB2⇒AB2=(152)2+(82)2=(7.5)2+(4)2=56.25+16⇒AB2=72.25⇒AB=√72.25⇒AB=8.5cm
Since it is a rhombus, the length of each side is 8.5 cm.
Question 25.
If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as .
 Discuss Question

:
Kite
In a kite, one diagonal of a the quadrilateral bisects the other.
Question 26.
Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are
a) 30∘,150∘,30∘,150∘
b) 85∘,95∘,85∘,95∘
c) 45∘,135∘,45∘,135∘
d) 30∘,180∘,30∘,180∘
 Discuss Question

:
Let the adjacent angles of a parallelogram be x and 5x, respectively.
Then, x+5x=180∘ [∵ adjacent angles of a parallelogram are supplementary]
⇒6x=180∘
⇒x=30∘
∴ The adjacent anlges are 30∘ and 150∘.
Hence, the angles are 30∘,150∘,30∘,150∘ . [∵ opposite angles are equal]
Question 27.
In a quadrilateral PQRS, ∠P=50∘,∠Q=50∘,∠R=60∘. Find ∠S. Is this quadrilateral convex or concave?
 Discuss Question

:
Given a quadrilateral PQRS, where
∠P=50∘,∠Q=50∘ and ∠R=60∘
Now, by the angle sum property of a quadrilateral, we have
∠P+∠Q+∠R+∠S=360∘⇒50∘+50∘+60∘+∠S=360∘⇒∠S=360∘−160∘⇒∠S=200∘
One interior angle of the given quadrilateral is greater than 180∘, therefore the quadrilateral is concave.
Question 28.
To construct a unique rectangle, the minimum number of measurements required is
(a) 4
(b) 3
(c) 2
(d) 1
 Discuss Question

:
Since, in a rectangle, opposite sides are equal and parallel, so we need the measurement of only two adjacent sides, i.e. length and breadth. Also, each angle measures 90∘.
Hence, we require only two measurements to construct a unique rectangle.
Question 29.
Is A Closed Curve Entirely Made Up Of Line Segments. The An... is a closed curve entirely made up of line segments. The another name for this shape is ___.
 Discuss Question

:
Concave polygon
As one interior angle is of greater than 180∘.
Question 30.
A rectangle MORE is shown below.
A Rectangle MORE Is Shown Below.Answer The Following Questio...
Answer the following questions by giving appropriate reason.
Is ∠MYO=∠RXE?
 Discuss Question

:
Yes, ∠MYO=∠RXE
Here, MY and RX are perpendicular to OE.
Since, ∠RXO=90∘⇒∠RXE=90∘ and ∠MYE=90∘⇒∠MYO=90∘.

Latest Videos
Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)
Direction Sense Test Part 1 Reasoning (Hindi)
Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE
Cube & Cuboid Part 1 Reasoning (Hindi)
Data Interpretation (DI) Basic Concept Reasoning (Hindi)
Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)
Sail E0 free webinar Webinars
Real Numbers Part 7 Class 10 Maths
Real Numbers Part 1 Class 10 Maths
Polynomials Part 1 Class 10 Maths

Latest Test Papers

DSP Combined 1 Free Revision Test SAIL JO E-0
GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0
BSP Plant Specific Review Test SAIL JO E-0
BSL Combined 1 Free Revision Test SAIL JO E-0
GFM Combined 1 Free Revision Test SAIL JO E-0