Quadrilaterals Test

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Quadrilaterals Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

If a Quadrilateral ABCD, AB ∥CD, then ABCD is a

A
Parallelogram

B
Rectangle

C
Trapezium

D
Square

Solution

A quadrilateral with only one pair of opposite sides parallel is called Trapezium.
Question 2
1 / -0

ABCD is a Rhombus such that ∠ACB= 40∘∘, then ∠ADB is

A
60^∘

B
40^∘

C
100^∘

D
50^∘

Solution

In Rhombus, digonals bisect each other right angle. By using angle sum property in any of the four triangles formed by intersection of diagonals, we get angle CBD = 50 and angle CBD = angle ADC ( alternate angles).

So, angle ADC = 50
Question 3
1 / -0

The Quadrilateral formed by joining the mid-points of the sides of a Quadrilateral PQRS, taken in order, is a rectangle if

A
PQRS is a Parallelogram

B
PQRS is a Rectangle

C
Diagonals of PQRS are at right angles.

D
None of these

Solution

Diagonals of PQRS are at right angles forms all the internal angles as right angles.(according to angle property of rectangle, i.e; all the angles of a rectangle are right angle(90⁰)
Question 4
1 / -0

The Quadrilateral forms by joining the mid-points of the sides of a Quadrilateral PQRS, taken in order, is a Rhombus if

A
Diagonals of PQRS are equal

B
PQRS is a Parallelogram

C
PQRS is a Rhombus

D
None of these

Solution

A quadrilateral formed by joining the mid points of the sides of the Rectangle is a rhombus. In rectangle , diagonals are equal.
Question 5
1 / -0

Given 4 points A, B, C, D such that 3 Points A, B, C are collinear. By joining these points in order we get

A
A Rhombus

B
A Straight Line

C
A Rectangle

D
A Triangle

Solution

If three or more points lie on same line then they are called collinear points. A,B and C are collinear means they form a line. Point D is out side the line. Point D can be join with the end points of the line formed by points A,B and C. For this we need total three lines to form a closed figure. A closed figure with three sides is called triangle.
Question 6
1 / -0

In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is a

A
Kite

B
Triangle

C
Rhombus

D
Rectangle

Solution

A quadrilateral having equal adjancent sides is called Kite. AB and BC are adjancent sides and AD and DC are also adjancent sides which are equal.
Question 7
1 / -0

Given a triangular prism, then what can we conclude about the lateral faces?

A
Faces are Trapezium

B
Faces are rectangle

C
Faces are Parallelogram

D
Faces are Prism

Solution

There are five faces in triangular prism. two triangles and three quadrilaterals in which both pair of opposite sides equal. A quadrilateral with both pair of opposite sides equal is called parallelogram. So, lateral faces are parallelogram.
Question 8
1 / -0

Consecutive angles of a Parallelogram are

A
Equal

B
Supplementary

C
Acute

D
Complementary

Solution

In parallelogram, both pair of opposite sides are parallel. So, consecutive angles form a pair of co-interior angles. Cointerior angles add upto 180. It means they are supplementary.
Question 9
1 / -0

A diagonal of a Rectangle is inclined to one side of the rectangle at an angle of 25^∘. The Acute Angle between the diagonals is :

A
40^∘

B
115^∘

C
25^∘

D
50^∘

Solution

Two diagonals of a rectangle divides it into four triangles. Out of these four triangles a pair of opposite triangles are congruent by SSS in which a pair of triangles have two equal angles of 25 each and in another pair of opposite triangles have two equal angles of 65 each. By angle sum property we have two options of angle fromed between diagonals. Either it is of 130 or 50. 50 is an acute angle. So, it is a correct option.
Question 10
1 / -0

If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is a

A
Parallelogram

B
Triangle

C
Rhombus

D
Rectangle

Solution

Two diagonals of quadrilateral form four triangles. Out of these four triangles two triangles of opposite to each other are congruent by SAS. By using CPCT property we can prove that both pair of opposite sides in a quadrilateral are parallel. A quadrilateral with both pair of opposite sides parallel is called parallelogram.

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Quadrilaterals Test - 6

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Quadrilaterals Test - 6

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Question 1

Parallelogram

Rectangle

Trapezium

Square

Solution

Question 2

60∘

40∘

100∘

50∘

Solution

Question 3

PQRS is a Parallelogram

PQRS is a Rectangle

Diagonals of PQRS are at right angles.

None of these

Solution

Question 4

Diagonals of PQRS are equal

PQRS is a Parallelogram

PQRS is a Rhombus

None of these

Solution

Question 5

A Rhombus

A Straight Line

A Rectangle

A Triangle

Solution

Question 6

Kite

Triangle

Rhombus

Rectangle

Solution

Question 7

Faces are Trapezium

Faces are rectangle

Faces are Parallelogram

Faces are Prism

Solution

Question 8

Equal

Supplementary

Acute

Complementary

Solution

Question 9

40∘

115∘

25∘

50∘

Solution

Question 10

Parallelogram

Triangle

Rhombus

Rectangle

Solution

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60^∘

40^∘

100^∘

50^∘

40^∘

115^∘

25^∘

50^∘