Knowledge Check : Geometry
Knowledge Check – Geometry
Basic Geometrical Concepts
Q1: A point has
A) Length but no breadth
B) No length, breadth or thickness
C) Length and breadth
D) Only thickness
Q2: How many end points does a ray have?
A) Zero
B) One
C) Two
D) Infinite
Q3: The measure of a complete angle is
A) 90°
B) 180°
C) 270°
D) 360°
Q4: An angle greater than 180° but less than 360° is called
A) Acute
B) Obtuse
C) Reflex
D) Right
Q5: The common end point where two rays meet to form an angle is called
A) Arm
B) Vertex
C) Side
D) Base
Q6: The corner of a blackboard in a classroom forms which type of angle?
A) Acute
B) Right
C) Obtuse
D) Reflex
Q7: How many angles are formed when two straight lines intersect?
A) 2
B) 3
C) 4
D) Infinite
Q8: Vertically opposite angles are always
A) Equal
B) Supplementary
C) Complementary
D) Adjacent only
Q9: Two angles are complementary if their sum is
A) 90°
B) 180°
C) 270°
D) 360°
Q10: A linear pair of angles is always
A) Complementary
B) Supplementary
C) Equal
D) Acute
Q11: The instrument used to measure an angle is
A) Ruler
B) Divider
C) Protractor
D) Compass
Q12: Minimum number of sides a polygon can have is
A) 2
B) 3
C) 4
D) 5
Q13: Railway tracks represent
A) Line segments
B) Rays
C) Lines
D) Curves
Q14: Number of rays that can be drawn from a given point is
A) One
B) Two
C) Finite
D) Infinite
Q15: Which is an open curve?
A) Circle
B) Square
C) Parabola
D) Triangle
Q16: While measuring an angle with a protractor, the centre hole is placed on the
A) Midpoint of one arm
B) Vertex
C) Any point on the arm
D) Outside the angle
Q17: Adjacent supplementary angles form a
A) Right angle
B) Straight angle
C) Reflex angle
D) Complete angle
Q18: Angle between hands of a clock at 3 o’clock is
A) 60°
B) 90°
C) 120°
D) 180°
Q19: An angle of exactly 180° is called
A) Straight angle
B) Reflex angle
C) Obtuse angle
D) Acute angle
Q20: A transversal intersecting two parallel lines forms how many angles?
A) 4
B) 6
C) 8
D) 12
Lines and Pairs of Lines
Q21: Vertically opposite angles are always
A) Equal
B) Supplementary
C) Complementary
D) Adjacent only
Q22: Two lines are parallel if corresponding angles are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q23: Alternate interior angles are equal when the lines are
A) Intersecting
B) Parallel
C) Perpendicular
D) Skew
Q24: Consecutive interior angles are supplementary when lines are
A) Parallel
B) Intersecting
C) Perpendicular
D) None
Q25: Railway tracks in India are always
A) Parallel
B) Intersecting
C) Perpendicular
D) Skew
Q26: If two parallel lines are cut by a transversal, each pair of corresponding angles is
A) Equal
B) Supplementary
C) Complementary
D) Vertically opposite
Q27: In a pair of parallel lines, alternate interior angles are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q28: If a transversal makes equal corresponding angles with two lines, the lines are
A) Parallel
B) Perpendicular
C) Intersecting
D) Cannot say
Q29: Two lines that never meet and are not parallel are called
A) Perpendicular
B) Skew
C) Intersecting
D) Coplanar
Q30: When two parallel lines are intersected by a transversal, the number of pairs of supplementary angles formed is
A) 2
B) 4
C) 6
D) 8
Q31: Roads crossing at right angles are
A) Parallel
B) Perpendicular
C) Skew
D) Intersecting but not perpendicular
Q32: In India, opposite lanes of a highway are
A) Parallel
B) Intersecting
C) Perpendicular
D) Skew
Q33: If two lines are parallel, then the distance between them is
A) Increasing
B) Decreasing
C) Constant
D) Zero
Q34: The number of parallel lines that can be drawn through a given point not on a line is
A) Zero
B) One
C) Two
D) Infinite
Q35: When two parallel lines are cut by a transversal, vertically opposite angles are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q36: In a pair of parallel lines, corresponding angles are
A) Equal
B) Supplementary
C) Complementary
D) Adjacent
Q37: Two lines that intersect to form 90° angles are called
A) Parallel
B) Perpendicular
C) Skew
D) Coplanar
Q38: The lines joining opposite corners of a cricket pitch are an example of
A) Parallel lines
B) Perpendicular lines
C) Intersecting lines
D) Skew lines
Q39: In a diagram, if alternate interior angles are equal, the lines must be
A) Parallel
B) Perpendicular
C) Intersecting
D) Cannot determine
Q40: The maximum number of parallel lines that can pass through a single point is
A) Zero
B) One
C) Two
D) Infinite
Triangles
Q41: The sum of all interior angles of a triangle is
A) 90°
B) 180°
C) 270°
D) 360°
Q42: A triangle having all sides equal is called
A) Isosceles
B) Scalene
C) Equilateral
D) Right-angled
Q43: In an isosceles triangle, the angles opposite the equal sides are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q44: A triangle with one angle greater than 90° is called
A) Acute
B) Right-angled
C) Obtuse
D) Equilateral
Q45: In a right-angled triangle, the longest side is
A) One of the legs
B) Hypotenuse
C) Altitude
D) Median
Q46: Exterior angle of a triangle is equal to the sum of its
A) Two adjacent interior angles
B) Two remote interior angles
C) All three interior angles
D) None
Q47: In a triangle, if two angles are 55° and 70°, the third angle is
A) 45°
B) 55°
C) 65°
D) 75°
Q48: A triangle with no two sides equal is called
A) Isosceles
B) Equilateral
C) Scalene
D) Right-angled
Q49: In a right-angled triangle, the two acute angles are always
A) Equal
B) Complementary
C) Supplementary
D) Obtuse
Q50: The Ashoka Chakra on the Indian flag contains how many triangles?
A) 12
B) 24
C) 36
D) 48
Q51: A triangle with angles 40°, 70°, 70° is
A) Scalene
B) Isosceles
C) Equilateral
D) Right-angled
Q52: In △ABC, if ∠A = 90°, then the side opposite to it is
A) AB
B) BC
C) AC
D) Hypotenuse BC
Q53: The side opposite the largest angle in a triangle is
A) Shortest
B) Longest
C) Median
D) Altitude
Q54: In △ABC, ∠B = 40°, ∠C = 60°, then ∠A =
A) 70°
B) 80°
C) 90°
D) 100°
Q55: A triangle with all angles less than 90° is called
A) Right-angled
B) Obtuse
C) Acute
D) Reflex
Q56: In an equilateral triangle, each angle measures
A) 45°
B) 60°
C) 90°
D) 120°
Q57: A triangle with angles 90°, 45°, 45° is
A) Isosceles right triangle
B) Scalene right triangle
C) Obtuse triangle
D) Equilateral
Q58: The number of obtuse angles a triangle can have is
A) 0
B) 1
C) 2
D) 3
Q59: In △PQR, if PQ = PR, then it is
A) Scalene
B) Isosceles
C) Equilateral
D) Right-angled
Q60: The triangle formed by joining the midpoints of the sides of a triangle has area
A) Same as original
B) Half of original
C) One-fourth of original
D) Double of original
Congruence and Similarity of Triangles
Q61: SSS criterion of congruence states that triangles are congruent if
A) Three angles are equal
B) Three sides are equal
C) Two sides and included angle are equal
D) Two angles and one side are equal
Q62: Which of the following is NOT a congruence criterion?
A) SAS
B) ASA
C) AAA
D) RHS
Q63: RHS congruence criterion is applicable only for
A) All triangles
B) Right-angled triangles
C) Isosceles triangles
D) Equilateral triangles
Q64: Ratio of areas of two similar triangles is 16:25. The ratio of their corresponding sides is
A) 2:5
B) 4:5
C) 16:25
D) 256:625
Q65: Basic Proportionality Theorem is also called
A) Pythagoras theorem
B) Thales’ theorem
C) Euler’s theorem
D) Ceva’s theorem
Q66: If △ABC ∼ △DEF, then
A) AB = DE
B) ∠A = ∠D
C) AC = DF
D) All are correct
Q67: ASA congruence means
A) Angle-Side-Angle
B) Angle-Angle-Side
C) Both A and B
D) None
Q68: In two triangles, if two angles of one are equal to two angles of the other, the triangles are
A) Congruent
B) Similar
C) Equal in area
D) Cannot say
Q69: If a line parallel to BC intersects AB at P and AC at Q, then by BPT
A) AP/AB = AQ/AC
B) AP/PB = AQ/QC
C) Both A and B
D) None
Q70: Triangles with sides 3 cm, 4 cm, 5 cm and 6 cm, 8 cm, 10 cm are
A) Congruent
B) Similar
C) Neither
D) Equal in area
Q71: SAS congruence requires
A) Two sides and non-included angle
B) Two sides and included angle
C) Two angles and included side
D) Three sides
Q72: If △ABC ≅ △PQR by SSS, then correspondence of vertices is
A) A→P, B→Q, C→R
B) A→Q, B→P, C→R
C) Any order
D) None
Q73: In similar triangles, corresponding angles are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q74: Perimeters of two similar triangles are 24 cm and 36 cm. Ratio of corresponding sides is
A) 2:3
B) 3:2
C) 4:9
D) 24:36
Q75: If △ABC ∼ △XYZ with ratio 3:5, then area ratio is
A) 3:5
B) 9:25
C) 27:125
D) 6:10
Q76: In △ABC, DE ∥ BC. Then △ADE ∼
A) △ABC
B) △ACB
C) △BCA
D) None
Q77: For two triangles to be congruent by AAS, we need
A) Two angles and included side
B) Two angles and non-included side
C) Three angles
D) Two sides
Q78: If three angles of one triangle are equal to three angles of another, the triangles are
A) Congruent
B) Similar
C) Equal in perimeter
D) Cannot say
Q79: Two triangles are congruent if
A) Three sides and three angles are equal
B) Three angles are equal
C) They satisfy any congruence criterion
D) Both A and C
Q80: If the ratio of corresponding sides of two similar triangles is 5:7, then ratio of their areas is
A) 5:7
B) 25:49
C) 10:14
D) 125:343
Polygons and Quadrilaterals
Q81: The sum of all interior angles of a quadrilateral is
A) 180°
B) 360°
C) 540°
D) 720°
Q82: A quadrilateral having exactly one pair of parallel sides is called
A) Parallelogram
B) Trapezium
C) Rhombus
D) Kite
Q83: Diagonals of a rhombus bisect each other at
A) 60°
B) 90°
C) 120°
D) Any angle
Q84: A square is a regular
A) Triangle
B) Quadrilateral
C) Pentagon
D) Hexagon
Q85: In a parallelogram, opposite sides are
A) Equal and parallel
B) Equal but not parallel
C) Parallel but not equal
D) Neither equal nor parallel
Q86: The diagonals of a rectangle are
A) Equal and bisect each other
B) Unequal and bisect each other
C) Equal but do not bisect
D) Perpendicular
Q87: A quadrilateral in which both pairs of opposite angles are equal is a
A) Kite
B) Trapezium
C) Parallelogram
D) Rhombus
Q88: All sides of a rhombus are
A) Equal
B) Unequal
C) Two pairs equal
D) Cannot say
Q89: A kite has
A) Two pairs of adjacent equal sides
B) Two pairs of opposite equal sides
C) All sides equal
D) No equal sides
Q90: The sum of interior angles of a pentagon is
A) 360°
B) 540°
C) 720°
D) 900°
Q91: Each interior angle of a regular pentagon is
A) 108°
B) 120°
C) 135°
D) 144°
Q92: A rectangle is a rhombus.
A) Is always
B) Is never
C) May be
D) Is not
Q93: In a parallelogram, consecutive angles are
A) Equal
B) Supplementary
C) Complementary
D) Right angles
Q94: The diagonals of a square are
A) Equal and perpendicular
B) Unequal and parallel
C) Equal but not perpendicular
D) Perpendicular but unequal
Q95: A quadrilateral whose all sides are equal and all angles are 90° is
A) Rectangle
B) Rhombus
C) Square
D) Kite
Q96: The number of sides in a regular hexagon is
A) 5
B) 6
C) 7
D) 8
Q97: Each interior angle of a regular hexagon measures
A) 108°
B) 120°
C) 135°
D) 144°
Q98: A parallelogram with all sides equal is a
A) Rectangle
B) Rhombus
C) Square
D) Trapezium
Q99: In a trapezium, the non-parallel sides are called
A) Legs
B) Bases
C) Diagonals
D) Heights
Q100: The sum of interior angles of an octagon is
A) 720°
B) 900°
C) 1080°
D) 1260°
3D Shapes
Q101: A cuboid has how many faces?
A) 4
B) 6
C) 8
D) 12
Q102: A cube has how many edges?
A) 6
B) 8
C) 12
D) 24
Q103: Euler’s formula for polyhedra is
A) F + V = E + 2
B) F + V – E = 2
C) F – V + E = 2
D) F × V = E
Q104: A matchbox is an example of
A) Cube
B) Cuboid
C) Cylinder
D) Cone
Q105: An Indian LPG gas cylinder is an example of
A) Cube
B) Cuboid
C) Cylinder
D) Sphere
Q106: A football is an example of
A) Cylinder
B) Cone
C) Sphere
D) Hemisphere
Q107: Total number of distinct nets possible for a cube is
A) 6
B) 8
C) 11
D) 12
Q108: A die (dice) is an example of
A) Cuboid
B) Cube
C) Cylinder
D) Pyramid
Q109: A cone has how many faces?
A) 1
B) 2
C) 3
D) 4
Q110: Number of vertices in a cuboid is
A) 6
B) 8
C) 12
D) 16
Q111: A pyramid with triangular base is called
A) Triangular pyramid
B) Tetrahedron
C) Both A and B
D) None
Q112: An ice-cream cone is an example of
A) Cylinder
B) Cone
C) Sphere
D) Hemisphere
Q113: A sphere has how many faces?
A) 0
B) 1
C) 2
D) Infinite
Q114: Number of edges in a cube is
A) 6
B) 8
C) 12
D) 24
Q115: A tent is an example of
A) Cylinder
B) Cone
C) Pyramid
D) Cuboid
Q116: Total surface area of a cuboid includes
A) 4 faces
B) 6 faces
C) Top and bottom only
D) Lateral only
Q117: A brick is an example of
A) Cube
B) Cuboid
C) Cylinder
D) Cone
Q118: Number of faces in a triangular prism is
A) 4
B) 5
C) 6
D) 9
Q119: A globe is an example of
A) Sphere
B) Hemisphere
C) Cylinder
D) Cone
Q120: For a cube, F = 6, V = 8, then E =
A) 10
B) 12
C) 14
D) 16
Circle and its Properties
Q121: The perpendicular from the centre to a chord
A) Bisects the chord
B) Is parallel to the chord
C) Touches the chord at one end
D) Does not intersect the chord
Q122: Equal chords of a circle are
A) Equidistant from the centre
B) Not equidistant
C) Parallel
D) Perpendicular
Q123: Angle subtended by a diameter in a semicircle is
A) 60°
B) 90°
C) 120°
D) 180°
Q124: Number of tangents that can be drawn from an external point to a circle is
A) 1
B) 2
C) 3
D) Infinite
Q125: The tangent at any point of a circle is perpendicular to the radius at the point of
A) Centre
B) Contact
C) Intersection
D) Secant
Q126: A chord that passes through the centre is called
A) Radius
B) Diameter
C) Tangent
D) Secant
Q127: The longest chord of a circle is
A) Radius
B) Diameter
C) Secant
D) Tangent
Q128: Angles in the same segment of a circle are
A) Equal
B) Supplementary
C) Complementary
D) Unequal
Q129: Number of circles that can be drawn passing through three non-collinear points is
A) 0
B) 1
C) 2
D) Infinite
Q130: Two tangents drawn from an external point to a circle are
A) Equal in length
B) Unequal
C) Perpendicular
D) Parallel
Q131: The region between a chord and the arc is called
A) Sector
B) Segment
C) Tangent
D) Radius
Q132: Angle subtended by an arc at the centre is
A) Half the angle at circumference
B) Equal to angle at circumference
C) Double the angle at circumference
D) None
Q133: A line intersecting a circle at two points is called
A) Tangent
B) Secant
C) Radius
D) Diameter
Q134: The inscribed angle is always
A) Greater than central angle
B) Equal to central angle
C) Half of central angle
D) Double central angle
Q135: If two chords are equal, then their corresponding arcs are
A) Equal
B) Unequal
C) Congruent
D) Parallel
Q136: The point inside the circle equidistant from all points on the circle is
A) Circumcentre
B) Centre
C) Incentre
D) Orthocentre
Q137: Maximum number of tangents that can be drawn at a point on the circle is
A) 0
B) 1
C) 2
D) Infinite
Q138: The area bounded by two radii and the arc is called
A) Segment
B) Sector
C) Chord
D) Tangent
Q139: Alternate segment theorem relates tangent and
A) Radius
B) Chord
C) Diameter
D) Centre
Q140: In a circle, the angle subtended by an arc at the centre is 120°. The angle subtended at the circumference is
A) 30°
B) 60°
C) 120°
D) 240°