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Class 10

Explore popular questions from Triangles for Class 10. This collection covers Triangles previous year Class 10 questions hand picked by experienced teachers.

Triangles

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Q 1. In the given figure {tex} \angle \mathrm { A } = 80 ^ { \circ } , \mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 2 \mathrm { x } ^ { \circ } {/tex} and {tex} \angle \mathrm { BDC } = \mathrm { y } ^ { \circ } , \mathrm { BD } {/tex} and {tex} \mathrm { CD } {/tex} bisect angles {tex} \mathrm { B } {/tex} and {tex} \mathrm { C } {/tex} respectively. The values of {tex} \mathrm { x } {/tex} and {tex} \mathrm { y } , {/tex} respectively, are

A

{tex} 15 ^ { \circ } , 70 ^ { \circ } {/tex}

B

{tex} 10 ^ { \circ } , 160 ^ { \circ } {/tex}

{tex} 20 ^ { \circ } , 130 ^ { \circ } {/tex}

D

{tex} 20 ^ { \circ } , 125 ^ { \circ } {/tex}

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Q 2. If {tex} a + b + c = 2 s , {/tex} then the value of {tex} ( s - a ) ^ { 2 } + ( s - b ) ^ { 2 } + ( s - c ) ^ { 2 } {/tex} will be:

A

{tex} s ^ { 2 } + a ^ { 2 } + b ^ { 2 } + c ^ { 2 } {/tex}

{tex} a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - s ^ { 2 } {/tex}

C

{tex} s ^ { 2 } - a ^ { 2 } - b ^ { 2 } - c ^ { 2 } {/tex}

D

{tex} 4 s ^ { 2 } - a ^ { 2 } - b ^ { 2 } - c ^ { 2 } {/tex}

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Q 3. If {tex} \mathrm { D } {/tex} is a point on the side {tex} \mathrm { BC } = 12 \mathrm { cm } {/tex} of a {tex} \Delta \mathrm { ABC } {/tex} such that {tex} \mathrm { BD } = 9 \mathrm { cm } {/tex} and {tex} \angle \mathrm { ADC } = \angle \mathrm { BAC } , {/tex} then the length of {tex} \mathrm { AC }{/tex} is equal to:

A

{tex} 9 \mathrm { cm } {/tex}

{tex} 6 \mathrm { cm } {/tex}

C

{tex} 6 \sqrt { 3 } {/tex}

D

{tex} 3 \mathrm { cm } {/tex}

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Q 4. In {tex} \triangle \mathrm { ABC } {/tex} medians {tex} \mathrm { BE } {/tex} and {tex} \mathrm { CF } {/tex} intersect at G. If the straightline {tex}\mathrm{AGD}{/tex} meets {tex} \mathrm { BC } {/tex} at {tex} \mathrm { D } {/tex} in such a way that {tex} \mathrm { GD } = 1.5 \mathrm { cm } , {/tex} then the length of {tex} \mathrm { AD } {/tex} is :

A

{tex} 2.5 \mathrm { cm } {/tex}

B

{tex} 3.0 \mathrm { cm } {/tex}

C

{tex} 4.00 \mathrm { cm } {/tex}

{tex} 4.5 \mathrm { cm } {/tex}

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Q 5. The side of an equilateral triangle is {tex} 20 \sqrt { 3 } \mathrm { cm } {/tex}. The numerical value of the radius of the circle circumscribing the triangle is :

{tex} 20 \mathrm { cm } {/tex}

B

{tex} 20 \sqrt { 3 } \mathrm { cm } {/tex}

C

{tex} 20 \pi \mathrm { cm } {/tex}

D

{tex} \frac { 20 } { \pi } {/tex}

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Q 6. If {tex} \Delta \mathrm { ABC } {/tex} is a right angled triangle with {tex} \angle \mathrm { A } = 90 ^ { \circ } , \mathrm { AN } {/tex} is perpendicular to {tex} \mathrm { BC } , \mathrm { BC } = 12 \mathrm { cm } {/tex} and {tex} \mathrm { AC } = 6 \mathrm { cm } {/tex} then the ratio of {tex} \frac { \text { area } \Delta \mathrm { ANC } } { \text { area } \Delta \mathrm { ABC } } {/tex}

A

1:3

B

1:2

1:4

D

1:8

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Q 7. The area of the largest triangle inscribed in a semi-circle of radius {tex} \mathrm { R } {/tex} is:

A

{tex} 2 \mathrm { R } ^ { 2 } {/tex}

{tex} \mathrm { R } ^ { 2 } {/tex}

C

{tex} \frac { 1 } { 2 } \mathrm { R } ^ { 2 } {/tex}

D

{tex} \frac { 3 } { 2 } \mathrm { R } ^ { 2 } {/tex}

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Q 8. In a triangle {tex}\mathrm{ABC}{/tex}, then sum of the exterior angles at {tex} \mathrm B {/tex} and {tex} \mathrm C {/tex} is equal to:

A

{tex} 180 ^ { \circ } - \angle \mathrm { BAC } {/tex}

{tex} 180 ^ { \circ } + \angle \mathrm { BAC } {/tex}

C

{tex} 180 ^ { \circ } - 2 \angle \mathrm { BAC } {/tex}

D

{tex} 180 ^ { \circ } + 2 \angle \mathrm { BAC } {/tex}

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Q 9. In {tex} \Delta \mathrm { ABC } , \angle \mathrm { B } = 3 \mathrm { x } , \angle \mathrm { A } = \mathrm { x } , \angle \mathrm { C } = \mathrm { y } {/tex} and {tex} 3 \mathrm { y } - 5 \mathrm { x } = 30 , {/tex} then the triangle is

A

isosceles

B

equlateral

right angled

D

scalene

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Q 10. The internal bisectors of {tex} \angle \mathrm { B } {/tex} and {tex} \angle \mathrm { C } {/tex} of {tex} \Delta \mathrm { ABC } {/tex} meet at {tex} \mathrm { O } . {/tex} If {tex} \angle \mathrm { A } = 80 ^ { \circ } , {/tex} then {tex} \angle \mathrm { BOC } {/tex} is:

A

{tex} 50 ^ { \circ } {/tex}

B

{tex} 100 ^ { \circ } {/tex}

{tex} 130 ^ { \circ } {/tex}

D

{tex} 160 ^ { \circ } {/tex}

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Q 11. Match the following (one to one)
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. Only One entries of column-I may have the matching with the some entries of column- II and one entry of column-II Only one matching with entries of column-I.
In the figure, the line segment xy is parallel to the side AC of {tex} \Delta \mathrm { ABC } {/tex} and it divides the triangle into two parts of equal areas, then match the column

{tex} ( \mathrm { A } - \mathrm { P } ){/tex}

B

{tex} ( \mathrm { B } - \mathrm { Q } ) {/tex}

C

{tex} (\mathrm C - \mathrm R ) {/tex}

D

{tex} (\mathrm D -\mathrm S ) {/tex}

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Q 12. The areas of two similar triangles are {tex} 12 \mathrm { cm } ^ { 2 } {/tex} and {tex} 48 \mathrm { cm } ^ { 2 } . {/tex} If the height of the smaller one is {tex} 2.1 \mathrm { cm } , {/tex} then the corresponding height of the bigger triangle is:

A

{tex} 12.6 \mathrm { cm } {/tex}

B

{tex} 8.4 \mathrm { cm } {/tex}

{tex} 4.2 \mathrm { cm } {/tex}

D

{tex} 1.05 \mathrm { cm } {/tex}

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Q 13. In a triangle {tex}DEF{/tex} shown in given figure, points {tex} A , B {/tex} and {tex} C {/tex} are taken on {tex}DE, DF{/tex} and {tex}EF{/tex} respectively, such that {tex} E C = A C {/tex} and {tex} C F = B C {/tex}. If angle {tex} D = 40 ^ { \circ } , {/tex} then what is angle {tex} A C B {/tex} in degrees?

A

140

B

70

100

D

None of these

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Q 14. {tex} \mathrm { AB } \perp \mathrm { BC } , \mathrm { BD } \perp \mathrm { AC } {/tex} and {tex} \mathrm { CE } {/tex} bisects {tex} \angle \mathrm { C. } {/tex} If {tex} \mathrm { A } = 30 ^ { \circ } . {/tex} Then, what is {tex} \angle \mathrm { CED } ? {/tex}

A

{tex} 30 ^ { \circ } {/tex}

{tex} 60 ^ { \circ } {/tex}

C

{tex} 45 ^ { \circ } {/tex}

D

{tex} 65 ^ { \circ } {/tex}

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Q 15. Express {tex} x {/tex} in terms of {tex} a , b , {/tex} and {tex} c {/tex}.

{tex} x = \frac { a c } { b + c } {/tex}

B

{tex} x = \frac { b c } { a + c } {/tex}

C

{tex} x = \frac { b + c } { a c } {/tex}

D

{tex} x = \frac { a b } { a + c } {/tex}

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Q 16. In {tex} \Delta \mathrm { ABC } , {/tex} if {tex} \mathrm { AD } \perp \mathrm { BC } {/tex} and {tex} \mathrm { AD } ^ { 2 } = \mathrm { BD } \times \mathrm { DC } . {/tex} Then find the angle {tex} \angle \mathrm { BAC } = ? {/tex}

A

{tex} 60 ^ { \circ } {/tex}

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

C

{tex} 30 ^ { \circ } {/tex}

D

None of this

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Q 17. {tex} \mathrm { PB } {/tex} and {tex} \mathrm { QA } {/tex} are perpendiculars to segment {tex}\mathrm {AB}{/tex}. If {tex} \mathrm { PO } = 5 \mathrm { cm } , {/tex} {tex} \mathrm { QO } = 7 \mathrm { cm } {/tex} and area {tex} \Delta \mathrm { POB } = 150 \mathrm { cm } ^ { 2 } , {/tex} find the area of {tex} \Delta \mathrm { QOA } {/tex}.

{tex} 294 \mathrm { cm } ^ { 2 } {/tex}

B

{tex} 150 \mathrm { cm } ^ { 2 } {/tex}

C

{tex} 250 \mathrm { cm } ^ { 2 } {/tex}

D

{tex} 210 \mathrm { cm } ^ { 2 } {/tex}

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Q 18. The corresponding altitude of two similar triangles are {tex} 6 \mathrm { cm } {/tex} and {tex} 9 \mathrm { cm } {/tex} respectively. Find the ratio of their areas.

A

9:4

B

3:2

4:9

D

8:16

Explanation

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Q 19. {tex} \mathrm { ABC } {/tex} is a triangle right-angled at {tex} \mathrm { C } {/tex} with {tex} \mathrm { BC } = \mathrm { a } {/tex} and {tex} \mathrm { AC } = \mathrm { b } . {/tex} If {tex} \mathrm { p } {/tex} is the length of the perpendicular from {tex} \mathrm { C } {/tex} on {tex} \mathrm { AB }{/tex} then.

A

{tex} \frac { 1 } { p ^ { 2 } } = \frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } {/tex}

B

{tex} p ^ { 2 } = \frac { a ^ { 2 } b ^ { 2 } } { a ^ { 2 } + b ^ { 2 } } {/tex}

C

{tex} \frac { 2 } { p ^ { 2 } } = \frac { a ^ { 2 } b ^ { 2 } } { a ^ { 2 } + b ^ { 2 } } {/tex}

Both A and B

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Q 20. {tex} \mathrm { ABC } {/tex} is a right triangle, right angled at {tex} \mathrm { C } , {/tex} let {tex} \mathrm { BC } = \mathrm { a } , \mathrm { CA } = \mathrm { b } , \mathrm { AB } = \mathrm { c } {/tex} and let p be the length of perpendicular from {tex} \mathrm { C } {/tex} on {tex} \mathrm { AB }{/tex}. Then which of the following is correct?

A

CP = AB

B

{tex} \frac { \mathrm { a } } { \mathrm { c } } = \frac { \mathrm { p } } { \mathrm { b } } {/tex}

C

CB = AP

Both (B) and (C)

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Q 21. Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in AD produced ME. Then which of the following is correct?

A

{tex} \mathrm { BL } = 2 \mathrm { EL } {/tex}

B

{tex} \mathrm { EL } = 2 \mathrm { BL } {/tex}

C

{tex} \mathrm { BE } = \frac1 2 \mathrm { EL } {/tex}

Both (B) and (C)

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Q 22. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is :

A

2:1

B

1:2

4:1

D

1:4

Explanation

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Q 23. Sides of two similar triangles are in the ratio {tex} 4: 9 . {/tex} Areas of these triangles are in the ratio:

A

2 : 3

B

4 : 9

C

81 : 16

16 : 81

Explanation

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Q 24. In the figure given below, {tex} \angle B A C = 90 ^ { \circ } {/tex} and {tex} A D \perp B C {/tex}. Then :

A

{tex} B D \times C D = B C ^ { 2 } {/tex}

B

{tex} A B \times A C = B C ^ { 2 } {/tex}

{tex} B D \times C D = A D ^ { 2 } {/tex}

D

{tex} A B \times A C = A D ^ { 2 } {/tex}

Explanation

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Q 25. If in two triangles {tex} A B C {/tex} and {tex} P Q R , \frac { A B } { Q R } = \frac { B C } { P R } = \frac { C A } { P Q } {/tex} then :

{tex} \Delta P Q R \sim \Delta C A B {/tex}

B

{tex} \Delta P Q R \sim \Delta A B C {/tex}

C

{tex} \Delta C B A \sim \Delta P Q R {/tex}

D

{tex} \Delta B C A \sim \Delta P Q R {/tex}

Explanation