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Class 9

Explore popular questions from Quadrilaterals for Class 9. This collection covers Quadrilaterals previous year Class 9 questions hand picked by experienced teachers.

Quadrilaterals

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Q 1. Match the following:

Column I Column II
(A) (P) CP = AQ
(B) (Q) PAQC is a parallelogram
(C) (R) AD = BC
(D) (S) PC {tex}\parallel{/tex} AQ

A

{tex} ( \mathrm { A } ) - ( \mathrm { P } , \mathrm { Q } , \mathrm { R } , \mathrm { S } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { P } , \mathrm { S } , \mathrm { R } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { P } , \mathrm { Q } , \mathrm { R } , \mathrm { S } ) {/tex}

All of the above

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Q 2. Smallest angle of a triangle is equal to two third the smallest angle of a quadrilateral. The ratio of the angles of the quadrilateral is 3 : 4 : 5 : 6. Largest angle of the triangle is twice its smallest angle. What is the sum of second largest angle of the triangle and the largest angle of the quadrilateral ?

A

160{tex}^\circ{/tex}

180{tex}^\circ{/tex}

C

190{tex}^\circ{/tex}

D

170{tex}^\circ{/tex}

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Q 3. The given figure,ABCD is a trapezium in which {tex}\angle{/tex}A= (x + 25){tex}^\circ{/tex}, {tex}\angle{/tex}B = y{tex}^\circ{/tex}, {tex}\angle{/tex}C = 95{tex}^\circ{/tex} and {tex}\angle{/tex}D = (2x +5){tex}^\circ{/tex}. Then the values of x and y are :

x = 50{tex}^\circ{/tex}, y = 85{tex}^\circ{/tex}

B

x = 45{tex}^\circ{/tex}, y = 85{tex}^\circ{/tex}

C

x = 40{tex}^\circ{/tex}, y = 90{tex}^\circ{/tex}

D

x = 92{tex}^\circ{/tex}, y = 60{tex}^\circ{/tex}

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Q 4. {tex} \mathrm { ABC } {/tex} is a triangle in which {tex} \mathrm { D } , \mathrm { E } {/tex} and {tex} \mathrm { F } {/tex} are the midpoints of {tex} \mathrm { AB } , \mathrm { BC } {/tex} and {tex} \mathrm { CA } {/tex} respectively. {tex} \mathrm {DE}{/tex}, {tex} \mathrm {EF}{/tex} and {tex} \mathrm { FD } {/tex} are joined. If {tex} \mathrm { AB } = 12 \mathrm { cm } , \mathrm { BC } = 13 \mathrm { cm } , {/tex} and {tex} \mathrm { AC } = 8 \mathrm { cm } . {/tex} Then the length of sides of triangle {tex} \mathrm {DEF}{/tex} are

{tex} \mathrm { DE } = 4 \mathrm { cm } , \mathrm { EF } = 6 \mathrm { cm } {/tex} and {tex} \mathrm { DF } = 6.5 \mathrm { cm } {/tex}

B

{tex} \mathrm { DE } = 6 \mathrm { cm } , \mathrm { DF } = 4 \mathrm { cm } , \mathrm { EF } = 6.5 \mathrm { cm } {/tex}

C

{tex} \mathrm { EF } = 4 \mathrm { cm } , \mathrm { DE } = 6.5 \mathrm { cm } , \mathrm { EF } = 6.5 \mathrm { cm } {/tex}

D

Cannot be determined

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Q 5. {tex} \mathrm { ABCD } {/tex} is a parallelogram. If {tex} \mathrm { P } {/tex} be a point on {tex} \mathrm { CD } {/tex} such that {tex} \mathrm { AP } = \mathrm { AD } {/tex}, then the measure of {tex} \angle \mathrm { PAB } + {/tex} {tex} \angle \mathrm { BCD } {/tex} is

{tex} 180 ^ { \circ } {/tex}

B

{tex} 225 ^ { \circ } {/tex}

C

{tex} 240 ^ { \circ } {/tex}

D

{tex} 135 ^ { \circ } {/tex}

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Q 6. If midpoints of a rectangle are joined, then
Assertion: The quadirilateral formed is necessarily a parallelogram.
Reason: Area of quadrilateral so formed is half the area of rectangle.

A

Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'

Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'

C

Assertion is true but Reason is false

D

Assertion is false but Reason is true

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Q 7. If {tex} \mathrm { ABCD } {/tex} is a parallalogram, then {tex} \angle \mathrm { A } - \angle \mathrm { C } {/tex} is

A

{tex} 180 ^ { \circ } {/tex}

{tex} 0 ^ { \circ } {/tex}

C

{tex} 360 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

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Q 8. In figure, if {tex} \mathrm { E } {/tex} and {tex} \mathrm { F } {/tex} are the midpoints of the sides of {tex} \mathrm { AB } {/tex} and {tex} \mathrm { CD } {/tex} of parallelogram {tex} \mathrm {ABCD}{/tex} respectively then which one of the following is/are true.

A

Line segment {tex} \mathrm {CE}{/tex} and {tex} \mathrm {AF}{/tex} trisects {tex} \mathrm {BD}{/tex}

B

{tex} \mathrm { AE } = \mathrm { CF } {/tex}

C

{tex} \Delta \mathrm { ADF } \cong \Delta \mathrm { CBE } {/tex}

All of the above

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Q 9. Which of the following statements is/ are true:

A

Diagonals of a rectangle are equal and bisect each other at {tex} 90 ^ { \circ } {/tex}

B

Diagonals of a square are equal and bisect each other at {tex} 90 ^ { \circ } {/tex}

C

Rhombus is a parallelogram with a pair of adjacent sides equal

Both (B) and (C)

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Q 10. Which of the following statements is/are true?

A

A rhombus has two pairs of equal angles.

B

Diagonals of a rectangle are equal and bisect each other

C

The diagonals of a square are of equal length

All of the above

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Q 11. In figure,{tex} \mathrm L{/tex}. {tex} \mathrm { M } {/tex} and {tex} \mathrm { N } {/tex} are the midpoints of {tex} \mathrm { AP } {/tex}, {tex} \mathrm {BP}{/tex} and {tex} \mathrm { CP } {/tex} respectively, then

A

{tex} \angle \mathrm { CAP } = \angle \mathrm { MNP } {/tex}

B

{tex} \angle \mathrm { ABP } = \angle \mathrm { NLP } {/tex}

C

{tex} \angle \mathrm { CAP } = \angle \mathrm { NMP } {/tex}

Both (A) and (B)

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Q 12. If in triangle {tex} \mathrm { XYZ } , \mathrm { XY } = \mathrm { XZ } {/tex} and {tex} \mathrm { M } , \mathrm { N } {/tex} are the midpoints of {tex} \mathrm { XY } , \mathrm { YZ } , {/tex} then which of the following is correct?

A

{tex} \mathrm { MN } = \frac { 1 } { 2 } \mathrm { YZ } {/tex}

B

{tex} \mathrm { MN } = \frac { 1 } { 2 } \mathrm { XZ } {/tex}

C

{tex} \mathrm { MN } = \mathrm { MX } = \mathrm { MY } {/tex}

Both (B) and (C)