651 + Interview Questions in GEOMETRY IN GENERAL AWARENESS Page 8 InterviewSolution

351.	The number of lines of symmetry in a 45o - 45o - 90o set-square is (A) 0 (B) 1 (C) 2 (D) 3
Answer» The correct answer is (B) 1

Discussion

352.	Fill in the blanks.(i) A line through two endpoints ‘A’ and ‘B’ is denoted by ______(ii) Aline segment from point ‘B’ to point ‘A’ is denoted by ______(iii) A ray has ______ endpoint(s).
Answer» (i) \(\overset {\leftrightarrow} {AB}\) (ii) \(\overline {BA}\) (iii) one

352.

Fill in the blanks.(i) A line through two endpoints ‘A’ and ‘B’ is denoted by (ii) Aline segment from point ‘B’ to point ‘A’ is denoted by (iii) A ray has __ endpoint(s).

Answer»

(i) \(\overset {\leftrightarrow} {AB}\)

(ii) \(\overline {BA}\)

(iii) one

Discussion

353.	In this Figure, ∠AYZ = 45°. If the point ‘A’ is shifted to point ‘B’ along the ray, then the measure of ∠BYZ is ____(a) more than 45°(b) 45°(c) less than 45°(d) 90°
Answer» The correct option is (b) 45°. ∠XYZ = ∠BYZ = ∠AYZ

353.

In this Figure, ∠AYZ = 45°. If the point ‘A’ is shifted to point ‘B’ along the ray, then the measure of ∠BYZ is ____(a) more than 45°(b) 45°(c) less than 45°(d) 90°

Answer»

The correct option is (b) 45°.

∠XYZ = ∠BYZ = ∠AYZ

Discussion

354.	The sides of a `DeltaABC ` measure 7 cm, 24 cm and 25cm. What type of a triangle is ABC ?
Answer» Since no two sides are equal, ABC is a scalene triangle. Further, `7^(2)+24^(2)=25^(2)` Since the square of the longest side is equal to the sum of the square of the other two sides, ABC is right-angled triangle.

Discussion

355.	In the figure above, `bar(PQ) and bar(RS)` are parallel. `bar(AC)` is transversal of `bar(PQ) and bar(RS)`. If `angle(ACP)=5x-70^(@) and angleBDR=4x+70^(@)`, then find the value of x.
Answer» Given that, `bar(PQ)"//"bar(RS) and bar(AB)` is a transversal. Aslo given, `angleACP=5x-70^(@) and angleBDR=4x+70^(@)`. `angleACP+angleBDR=180^(@)` (`:.` Exterior angles on the same side of the transversal.) `implies 5x-70^(@)+4x70^(@)=180^(@)` `implies 9x=180^(@)implies x=20^(@)`

Discussion

356.	What do you call the triangle whose two of its angles are `40^(@) and 70^(@)`A. ScaleneB. ObtuseC. IsoscelesD. Equilateral
Answer» Correct Answer - C Isosceles triangle Hence, the correct option is (c )

Discussion

357.	One pair of opposite angles of a parallelogram is `(2x-50^(@),x+20^(@))`. Then the parallelogram necessarily is _________A. a rhombusB. a squareC. a rectangleD. a trapezium
Answer» Correct Answer - C

Discussion

358.	If the supplementary angle of x is 4 times its complementary angle , then find x.
Answer» Correct Answer - `60^(@)`

Discussion

359.	In a rhombus, if diagonals are equal, then the rhombus necessarily will be ____A. a rectangle but not squareB. a squareC. a parallelogram but not a squareD. Kite
Answer» Correct Answer - B In a rhombus, if the diagonals are equal, then it becomes a square . Hence, the correct option is (b)

Discussion

360.	In a parallelogram, if the diagonals are equal, then the parallelogram necessarily will beA. a rhombusB. a rectangleC. a squareD. a trapezium
Answer» Correct Answer - B In a parallelogram , if the diagonals are equal, then it necessarily is a rectangle. Hence, the correct option is (b).

Discussion

361.	In the figure above, if l//m, then find `angleQPS+angleRPT`.
Answer» Correct Answer - `140^(@)`

Discussion

362.	In which of the following cases, a right triangle cannot be constructed ?A. 12 cm, 5cm, 13 cmB. 8 cm , 6 cm, 10 cmC. 5 cm , 9 cm , 11 cmD. 9 cm, 40 cm, 41 cm.
Answer» Correct Answer - C

Discussion

363.	Which of the following is the set of measures of the sides of triangle ?A. 8cm, 4 cm, 20 cmB. 9cm, 17 cm, 25cmC. 11 cm, 16cm, 28 cmD. 6cm, 7cm, 12 cm
Answer» Correct Answer - B

Discussion

364.	Name the two pairs of vertically opposite angles
Answer» ∠PTS and ∠QTR are vertically opposite angles. ∠PTR and ∠QTS are vertically opposite angles.

364.

Name the two pairs of vertically opposite angles

Answer»

∠PTS and ∠QTR are vertically opposite angles.

∠PTR and ∠QTS are vertically opposite angles.

Discussion

365.	For a given set of lines, it is possible to draw more than one transversal.
Answer» Yes, it is possible to draw more than one transversal for a given set of lines. l and m are given set of lines. n and p are transversal

Discussion

366.	Can two right angles form a linear pair?
Answer» Yes, because the sum of two right angles is 180° and form a linear pair.

Discussion

367.	Which of the following holds true ?A. The geometric centre of a triangle equidistant from its sides is called in centre or excentre.B. The centroid divides each median in the ratio 2:1 from the vertex.C. Both (a) and (b)D. Neither (a) or (b)
Answer» Correct Answer - C The geometric centre of a triangle equidistant from its sides is called incentre or excentre. The centroid divides each median in the ratio of `2:1` from the vertex. Hence, the correct option is ( c).

Discussion

368.	If all the sides are equal , then the quadrilateral must be ______
Answer» square, rhombus

Discussion

369.	In a quadrilateral ABCD, `bar(AC) bot bar(BD)` and AB=AD. ABCD is a ________A. trapeziumB. rhombusC. rectangleD. Kite
Answer» Correct Answer - D The given quadrilateral is a kite. Hence, the correct option is (d).

Discussion

370.	A triangle in which the sum of the squares of two side equals the square of the third side must be a/an ____ triangle.A. right angledB. aute angledC. obtuse angledD. None of these
Answer» Correct Answer - A Option (a) follows ( Pythagoras theorem ). Hence, the correct option is (a).

Discussion

371.	Find `angleDBA, angleDAB` and `angleAED` in the following figure, where ABCDE is a semi-circle.
Answer» `angleABD=40^(@)` `angleDAB=50^(@)` `angleAED=140^(@)`

Discussion

372.	In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x. A. `15^@`B. `30^@`C. `45^@`D. `60^@`
Answer» Correct Answer - D `BC=CD =EC` and proceed using `angle ECD=90^@+60^@=150^@`.

Discussion

373.	In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x. A. `15^@`B. `30^@`C. `45^@`D. `60^@`
Answer» Correct Answer - D `BC=CD =EC` and proceed using `angle ECD=90^@+60^@=150^@`.

Discussion

374.	In the given figure, if l//m , then what type of a triangle is ABC ? A. EquilateralB. IsoscelesC. ScaleneD. Right angled.
Answer» Correct Answer - B Given `l\|\|m` , `angleBCA=angleDEC=80^(@)` ( corresponding angles ) `angleCBA=angleEDB=50^(@)` ( corresponding angles ) `angleBCA+angleCBA+angleBAC=180^(@)` `implies 80^(@)+50^(@)+angleBAC=180^(@)` `implies angleBAC=50^(@)` `:.` In `DeltaABC, angleA=angleB=50` `implies DeltaABC` is isosceles. Hence, the correct option is (b).

Discussion

375.	If the angles of a linear pair are equal, then each angle is _____A. `30^(@)`B. `45^(@)`C. `60^(@)`D. `90^(@)`
Answer» Correct Answer - D `x+x=180^(@)` `implies x=90^(@)` Hence, the correct option is (d).

Discussion

376.	In the figure above, `angleABC=60^(@)`. Find x.
Answer» Correct Answer - `50^(@)`

Discussion

377.	Which of the following must be a square ?A. A rhombus whose adjacent angler are equal.B. A rectangle whose adjacent sides are equal .C. Both (a) and (b)D. Neither (a) or (b)
Answer» Correct Answer - C A rhombus whose adjacent angles are equal. `:.` Each angle would be `90^(@)`. Such a rhombus would be a square. A rectangle , whose adjacent side are equal, would have all sides equal. `:.` Such a rectangle would be a square. Hence, the correct option is (c ).

Discussion

378.	In a triangle PQR, if `angleQ` is obtuse and S is the orthocentre of `DeltaPQR`, then find the orthocentre of `DeltaPSR`.
Answer» Correct Answer - Q

Discussion

379.	The measure of the side of a `DeltaPQR` are integers in cm. If two of its sides are 1 cm each. Find the perimeter of the triangle.A. 3cmB. 4 cmC. 5 cmD. 6 cm
Answer» Correct Answer - A Perimeter =(1+1+1) cm = 3 cm Hence, the correct option is (a).

Discussion

380.	The measure of one of the exterior angles of a triangle is `100^(@)`. Which of the following is definitely the measure of one of the interior of that triangle?A. `50^(@)`B. `60^(@)`C. `70^(@)`D. `80^(@)`
Answer» Correct Answer - D If the measure of one of the exterior angles is `100^(@)`, then its supplement is the measure of one of the interior angles of the triangle. The measure of the required angle `=180^(@)-100^(@)=80^(@)` Hence, the correct option is (d).

Discussion

381.	If in a triangle, the circumcentre does not lie on its longest side , then it must be an/a_____ triangle .A. acute angledB. right angledC. obtuse angledD. Either (a) or (c )
Answer» Correct Answer - D For an acute-angled triangle, the circumcentre lies interior of it. For a right-angled triangle, it lies on its longest side. For an obtuse- angled triangle, it lies exterior of it. In the given problem, the circumcentre does not lies on the logest side. `:.` It is not righ angled. It can be either acute angled or obtuse angled. Hence, the correct optiond is (d).

Discussion

382.	All equilateral triangles are isosceles also.
Answer» All equilateral triangles are isosceles also.- True

Discussion

383.	Two non-parallel line segments will always intersect.
Answer» False (Hint: They will intersect, when they are produced)

Discussion

384.	Many lines can pass through two given points.
Answer» The correct answer is False.

Discussion

385.	Two angles can have exactly five points in common.
Answer» The correct answer is False.

Discussion

386.	State whether the statement are true (T) or false (F):If the arms of an angle on the paper are increased, the angle increases.
Answer» False. The angle is not affected, if the arms of an angle on the paper are increased or decreased.

386.

State whether the statement are true (T) or false (F):If the arms of an angle on the paper are increased, the angle increases.

Answer»

False.

The angle is not affected, if the arms of an angle on the paper are increased or decreased.

Discussion

387.	In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find (i) ∠DGC (ii) ∠DEF
Answer» We have AB\|\|ED and BC \|\| EF (i) BC is transversal ∠DGC = ∠ABC [corresponding angles] But ∠ABC = 70° ∠DGC = 70° (ii) ED is a transversal to BC\|\|EF ∴ ∠DEF = ∠DGC [corresponding] ∠DGC = 70° ∠DEF = 70°

387.

In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find (i) ∠DGC (ii) ∠DEF

Answer»

We have AB||ED and BC || EF

(i) BC is transversal

∠DGC = ∠ABC [corresponding angles]

But ∠ABC = 70°

∠DGC = 70°

(ii) ED is a transversal to BC||EF

∴ ∠DEF = ∠DGC [corresponding]

∠DGC = 70°

∠DEF = 70°

Discussion

388.	If the arms of an angle on the paper are decreased, the angle decreases.
Answer» The correct answer is False.

388.

If the arms of an angle on the paper are decreased, the angle decreases.

Answer»

The correct answer is False.

Discussion

389.	The angles of quadrilateral are `x-5^(@),x,x+5^(@),and x+10^(@)`. Find the smallest angle of the quadrilateral.
Answer» Correct Answer - `(82(1)/(2))^(@)`

Discussion

390.	In the figure above, ABCD is a parallelogram , and if AC=30 cm and BD=20 cm, find CP+DP.
Answer» Correct Answer - 25 cm

Discussion

391.	In the following figure, If l and m are two tangents and AB is a chord making and angle of `60^@` with the tangent l, then the angle between l and m is __________. A. `45^@`B. `30^@`C. `60^@`D. `90^@`
Answer» Correct Answer - C Tragents drawn to a circle from an external point are equal.

Discussion

392.	The locus of the point P which is at a constant distance of 2 units from the origin and which lies in the first or the second quadrants is __________.A. `y=-sqrt(4-x^2)`B. `y=sqrt(4-x^2)`C. `x=sqrt(4-y^2)`D. `x=-sqrt(4-y^2)`
Answer» Correct Answer - B Recall the definition of locus. In the first on the second quadrant, `gamma` is positive.

Discussion

393.	If PAB is a triangle in which `angle B=90^@ ` and `A(1,1) and B(0.1)` then the locus of P is __________.A. `Y=0`B. `xy=0`C. `x=y`D. `x=0`
Answer» Correct Answer - D Apply Pythagoras theorem.

Discussion

394.	In the following figure, O is the centre of the circle and `angle AMB=120^@` , Find the angle between the two tangents AP and BP. A. `30^@`B. `45^@`C. `70^@`D. `60^@`
Answer» Correct Answer - D Recall the properties of cyclic quadrilateral and also of tangents. `angle BOA +angle BPA=180^@ and angle BOA =2angle BQA`.

Discussion

395.	In the given figure, AB is the diameter and `/_ADC = 2 /_BDC`. If `/_ BCD =70^(@)`, then find the angle made by AC at the centre of the circle.
Answer» Correct Answer - `100^(@)`

Discussion

396.	The angles of a quadrilateral ABCD are `x^(@),(x+1)^(@),(x+2)^(@)` and `(x+3)^(@)`, taken in the same order. Then the quadrilateral ABCD is necessarily a
Answer» Correct Answer - Trapezium

Discussion

397.	In the following figure, if the angle between two chords AB and AC is `65^@` , then the angle between two tangents which are drawn at B and C is __________ A. `50^@`B. `30^@`C. `60^@`D. `40^@`
Answer» Correct Answer - A Radius is perpendicular to the tangent at the point of contact. In the quadrilateral `BOCP, angle BOC+angle BPC =180^@`.

Discussion

398.	In the above figure, AB is parallel to CD. P and R are the points on AB and CD respectively. Q is in between AB and CD. Find the value of x in degrees
Answer» Correct Answer - `50^(@)`

Discussion

399.	AB and CD are equal and parallel chords of a circle with centre O. Then AC passes through the centre O. [Agree `//` Disagree]
Answer» Correct Answer - Disagree

Discussion

400.	If three equal chords meet at three distinct points on the circle, then the angle between any two chords is `____________`.
Answer» Correct Answer - `60^(@)`

Discussion

Explore topic-wise InterviewSolutions in .

The number of lines of symmetry in a 45o - 45o - 90o set-square is (A) 0 (B) 1 (C) 2 (D) 3

Fill in the blanks.(i) A line through two endpoints ‘A’ and ‘B’ is denoted by ______(ii) Aline segment from point ‘B’ to point ‘A’ is denoted by ______(iii) A ray has ______ endpoint(s).

In this Figure, ∠AYZ = 45°. If the point ‘A’ is shifted to point ‘B’ along the ray, then the measure of ∠BYZ is ____(a) more than 45°(b) 45°(c) less than 45°(d) 90°

The sides of a `DeltaABC ` measure 7 cm, 24 cm and 25cm. What type of a triangle is ABC ?

In the figure above, `bar(PQ) and bar(RS)` are parallel. `bar(AC)` is transversal of `bar(PQ) and bar(RS)`. If `angle(ACP)=5x-70^(@) and angleBDR=4x+70^(@)`, then find the value of x.

What do you call the triangle whose two of its angles are `40^(@) and 70^(@)`A. ScaleneB. ObtuseC. IsoscelesD. Equilateral

One pair of opposite angles of a parallelogram is `(2x-50^(@),x+20^(@))`. Then the parallelogram necessarily is _________A. a rhombusB. a squareC. a rectangleD. a trapezium

If the supplementary angle of x is 4 times its complementary angle , then find x.

In a rhombus, if diagonals are equal, then the rhombus necessarily will be ____A. a rectangle but not squareB. a squareC. a parallelogram but not a squareD. Kite

In a parallelogram, if the diagonals are equal, then the parallelogram necessarily will beA. a rhombusB. a rectangleC. a squareD. a trapezium

In the figure above, if l//m, then find `angleQPS+angleRPT`.

In which of the following cases, a right triangle cannot be constructed ?A. 12 cm, 5cm, 13 cmB. 8 cm , 6 cm, 10 cmC. 5 cm , 9 cm , 11 cmD. 9 cm, 40 cm, 41 cm.

Which of the following is the set of measures of the sides of triangle ?A. 8cm, 4 cm, 20 cmB. 9cm, 17 cm, 25cmC. 11 cm, 16cm, 28 cmD. 6cm, 7cm, 12 cm

Name the two pairs of vertically opposite angles

For a given set of lines, it is possible to draw more than one transversal.

Can two right angles form a linear pair?

Which of the following holds true ?A. The geometric centre of a triangle equidistant from its sides is called in centre or excentre.B. The centroid divides each median in the ratio 2:1 from the vertex.C. Both (a) and (b)D. Neither (a) or (b)

If all the sides are equal , then the quadrilateral must be ______

In a quadrilateral ABCD, `bar(AC) bot bar(BD)` and AB=AD. ABCD is a ________A. trapeziumB. rhombusC. rectangleD. Kite

A triangle in which the sum of the squares of two side equals the square of the third side must be a/an ____ triangle.A. right angledB. aute angledC. obtuse angledD. None of these

Find `angleDBA, angleDAB` and `angleAED` in the following figure, where ABCDE is a semi-circle.

In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x. A. `15^@`B. `30^@`C. `45^@`D. `60^@`

In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x. A. `15^@`B. `30^@`C. `45^@`D. `60^@`

In the given figure, if l//m , then what type of a triangle is ABC ? A. EquilateralB. IsoscelesC. ScaleneD. Right angled.

If the angles of a linear pair are equal, then each angle is _____A. `30^(@)`B. `45^(@)`C. `60^(@)`D. `90^(@)`

In the figure above, `angleABC=60^(@)`. Find x.

Which of the following must be a square ?A. A rhombus whose adjacent angler are equal.B. A rectangle whose adjacent sides are equal .C. Both (a) and (b)D. Neither (a) or (b)

In a triangle PQR, if `angleQ` is obtuse and S is the orthocentre of `DeltaPQR`, then find the orthocentre of `DeltaPSR`.

The measure of the side of a `DeltaPQR` are integers in cm. If two of its sides are 1 cm each. Find the perimeter of the triangle.A. 3cmB. 4 cmC. 5 cmD. 6 cm

The measure of one of the exterior angles of a triangle is `100^(@)`. Which of the following is definitely the measure of one of the interior of that triangle?A. `50^(@)`B. `60^(@)`C. `70^(@)`D. `80^(@)`

If in a triangle, the circumcentre does not lie on its longest side , then it must be an/a_____ triangle .A. acute angledB. right angledC. obtuse angledD. Either (a) or (c )

All equilateral triangles are isosceles also.

Two non-parallel line segments will always intersect.

Many lines can pass through two given points.

Two angles can have exactly five points in common.

State whether the statement are true (T) or false (F):If the arms of an angle on the paper are increased, the angle increases.

In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find (i) ∠DGC (ii) ∠DEF

If the arms of an angle on the paper are decreased, the angle decreases.

The angles of quadrilateral are `x-5^(@),x,x+5^(@),and x+10^(@)`. Find the smallest angle of the quadrilateral.

In the figure above, ABCD is a parallelogram , and if AC=30 cm and BD=20 cm, find CP+DP.

In the following figure, If l and m are two tangents and AB is a chord making and angle of `60^@` with the tangent l, then the angle between l and m is __________. A. `45^@`B. `30^@`C. `60^@`D. `90^@`

The locus of the point P which is at a constant distance of 2 units from the origin and which lies in the first or the second quadrants is __________.A. `y=-sqrt(4-x^2)`B. `y=sqrt(4-x^2)`C. `x=sqrt(4-y^2)`D. `x=-sqrt(4-y^2)`

If PAB is a triangle in which `angle B=90^@ ` and `A(1,1) and B(0.1)` then the locus of P is __________.A. `Y=0`B. `xy=0`C. `x=y`D. `x=0`

In the following figure, O is the centre of the circle and `angle AMB=120^@` , Find the angle between the two tangents AP and BP. A. `30^@`B. `45^@`C. `70^@`D. `60^@`

In the given figure, AB is the diameter and `/_ADC = 2 /_BDC`. If `/_ BCD =70^(@)`, then find the angle made by AC at the centre of the circle.

The angles of a quadrilateral ABCD are `x^(@),(x+1)^(@),(x+2)^(@)` and `(x+3)^(@)`, taken in the same order. Then the quadrilateral ABCD is necessarily a

In the following figure, if the angle between two chords AB and AC is `65^@` , then the angle between two tangents which are drawn at B and C is __________ A. `50^@`B. `30^@`C. `60^@`D. `40^@`

In the above figure, AB is parallel to CD. P and R are the points on AB and CD respectively. Q is in between AB and CD. Find the value of x in degrees

AB and CD are equal and parallel chords of a circle with centre O. Then AC passes through the centre O. [Agree `//` Disagree]

If three equal chords meet at three distinct points on the circle, then the angle between any two chords is `____________`.

Fill in the blanks.(i) A line through two endpoints ‘A’ and ‘B’ is denoted by (ii) Aline segment from point ‘B’ to point ‘A’ is denoted by (iii) A ray has __ endpoint(s).