8th Grade > Mathematics
UNDERSTANDING QUADRILATERALS MCQs
Total Questions : 464
| Page 1 of 47 pages
:
False
In a trapezium, only one pair of sides is parallel.
:
Given, an isosceles trapezium, where AB∥DC, AD = BC and ∠A=60∘.
Then, ∠B=60∘.
Draw a line parallel to BC through D which intersects the line AB at E (say).
Then, DEBC is a parallelogram, where
BE = CD = 20 cm and DE = BC = 10 cm
Now, ∠DEB+∠CBE=180∘
[adjacent angles are supplementary in parallelogram]
⇒∠DEB=180∘−60∘=120∘
∴InΔADE,∠ADE=60∘ [exterior angle]
Also, ∠DEA=60∘ [∵ AD = DE = 10cm and ∠DAE=60∘]
Then, ΔADE is an equilateral triangle.
∴AE=10cm
⇒AB=AE+EB=10+20=30cm
Hence, x = 30 cm.
:
Supplementary
By property of a parallelogram, we know that the adjacent angles of a parallelogram are supplementary.
:
Angles
In a regular polygon, all sides are equal and all angles are equal.
Answer: Option B. -> Square
:
B
A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.
The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.
A rhombus has equal sides but not equal angles.
A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.
A square has equal sides and equal angles. Hence, it is a regular polygon.
:
B
A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.
The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.
A rhombus has equal sides but not equal angles.
A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.
A square has equal sides and equal angles. Hence, it is a regular polygon.
Answer: Option C. -> 37.6 cm
:
C
Let ‘a’ be one side of the kite = 7.8 cm
and‘b’ be the other side of the kite = 11 cm
Perimeter of the kite = 2a + 2b units
=2×7.8+2×11=15.6+22=37.6cm
:
C
Let ‘a’ be one side of the kite = 7.8 cm
and‘b’ be the other side of the kite = 11 cm
Perimeter of the kite = 2a + 2b units
=2×7.8+2×11=15.6+22=37.6cm