Geometry - Question Bank

1. What is the distance between two parallel lines?
A) The length of the perpendicular segment connecting them
B) The length of any segment connecting them
C) The sum of their lengths
D) Zero
2. In similar triangles, the ratio of their corresponding sides is equal to the ratio of their:
A) Areas
B) Perimeters
C) Altitudes
D) All of the above
3. If two triangles are similar, their corresponding angles are:
A) Proportional
B) Equal
C) Supplementary
D) Complementary
4. What is the ratio of the circumference of a circle to its diameter?
A) r
B) 2r
C) π
D) 2π
5. What is the total number of diagonals in a polygon with 'n' sides?
A) n * (n-1) / 2
B) n * (n-3) / 2
C) n * (n-2) / 2
D) n * (n-4) / 2
6. What is the relationship between the angle at the center and the angle at the circumference subtended by the same arc in a circle?
A) The central angle is half the circumference angle
B) The central angle is equal to the circumference angle
C) The central angle is double the circumference angle
D) There is no fixed relationship
7. A triangle with all three sides of different lengths is called a:
A) Isosceles triangle
B) Equilateral triangle
C) Scalene triangle
D) Right-angled triangle
8. What is the measure of an angle inscribed in a semicircle?
A) 45 degrees
B) 60 degrees
C) 90 degrees
D) 180 degrees
9. In a cyclic quadrilateral, the sum of opposite angles is:
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees
10. What is the area of a triangle with sides a, b, and c, and semi-perimeter s, using Heron's formula?
A) sqrt(s * (s-a) * (s-b) * (s-c))
B) s * (s-a) * (s-b) * (s-c)
C) sqrt(s + (s-a) + (s-b) + (s-c))
D) (s-a) * (s-b) * (s-c)
11. The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is:
A) Twice the length of the third side
B) Half the length of the third side
C) Equal in length to the third side
D) Unrelated to the third side
12. What is the angle formed by a tangent and a radius drawn to the point of tangency?
A) 0 degrees
B) 45 degrees
C) 90 degrees
D) 180 degrees
13. A line segment passing through the center of a circle and whose endpoints lie on the circle is called a:
A) Radius
B) Chord
C) Tangent
D) Diameter
14. Which of the following is NOT a type of triangle based on angles?
A) Acute triangle
B) Obtuse triangle
C) Isosceles triangle
D) Right-angled triangle
15. What is the perimeter of a square with side length 's'?
A) s^2
B) 4 * s
C) 2 * s
D) s
16. The sum of the angles in a quadrilateral is:
A) 180 degrees
B) 270 degrees
C) 360 degrees
D) Depends on the type of quadrilateral
17. What geometric shape has two parallel sides of unequal length and two non-parallel sides?
A) Rhombus
B) Parallelogram
C) Trapezoid
D) Rectangle
18. If two angles of a triangle are 45 degrees and 60 degrees, what is the third angle?
A) 60 degrees
B) 75 degrees
C) 90 degrees
D) 105 degrees
19. What is the measure of a central angle subtended by an arc that is one-third of the circumference of a circle?
A) 60 degrees
B) 90 degrees
C) 120 degrees
D) 180 degrees
20. A quadrilateral with at least one pair of parallel sides is called a:
A) Rhombus
B) Trapezoid
C) Kite
D) Parallelogram
21. What is the area of a parallelogram with base 'b' and height 'h'?
A) 0.5 * b * h
B) b + h
C) b * h
D) 2 * (b + h)
22. If a line segment divides a triangle into two smaller triangles of equal area, the line segment must be a:
A) Altitude
B) Median
C) Angle bisector
D) Perpendicular bisector
23. A triangle where one angle is greater than 90 degrees is called an:
A) Acute triangle
B) Obtuse triangle
C) Right-angled triangle
D) Isosceles triangle
24. What is the length of the diagonal of a square with side length 's'?
A) s
B) s * sqrt(2)
C) s / sqrt(2)
D) 2 * s
25. In an isosceles triangle, the angles opposite the equal sides are:
A) Different
B) Equal
C) Right angles
D) Obtuse
26. What is the sum of the exterior angles of any convex polygon?
A) 180 degrees
B) 270 degrees
C) 360 degrees
D) Depends on the number of sides
27. A rhombus with all angles equal to 90 degrees is a:
A) Parallelogram
B) Trapezoid
C) Square
D) Rectangle
28. What is the area of a rectangle with length 'l' and width 'w'?
A) 2 * (l + w)
B) l + w
C) l * w
D) 2 * l * w
29. What is the perimeter of a rectangle with length 'l' and width 'w'?
A) l * w
B) 2 * (l + w)
C) l + w
D) 2 * l * w
30. A triangle with angles 30, 60, and 90 degrees is a type of:
A) Acute triangle
B) Obtuse triangle
C) Right-angled triangle
D) Equilateral triangle
31. What is the measure of each exterior angle of a regular pentagon?
A) 72 degrees
B) 90 degrees
C) 108 degrees
D) 120 degrees
32. If two parallel lines are intersected by a transversal, the alternate interior angles are:
A) Supplementary
B) Complementary
C) Equal
D) None of the above
33. What is the relationship between the angles in a linear pair?
A) They are equal
B) Their sum is 90 degrees
C) Their sum is 180 degrees
D) Their sum is 360 degrees
34. A line that touches a circle at exactly one point is called a:
A) Chord
B) Secant
C) Tangent
D) Radius
35. What is a polygon with 5 sides called?
A) Hexagon
B) Heptagon
C) Pentagon
D) Octagon
36. The area of a circle with radius 'r' is given by the formula:
A) 2 * π * r
B) π * r
C) π * r^2
D) 2 * π * r^2
37. The formula for the circumference of a circle with radius 'r' is:
A) π * r
B) 2 * π * r
C) π * r^2
D) 2 * π * r^2
38. What is the diameter of a circle if its radius is 7 cm?
A) 3.5 cm
B) 7 cm
C) 14 cm
D) 49 cm
39. The distance from the center of a circle to any point on its circumference is called the:
A) Diameter
B) Radius
C) Circumference
D) Chord
40. A line segment that connects two points on a circle is called a:
A) Radius
B) Diameter
C) Tangent
D) Chord
41. What is the measure of each interior angle of a regular hexagon?
A) 100 degrees
B) 120 degrees
C) 135 degrees
D) 144 degrees
42. The sum of the interior angles of a polygon with 'n' sides is given by the formula:
A) (n-2) * 180 degrees
B) n * 180 degrees
C) (n-1) * 180 degrees
D) (n+2) * 180 degrees
43. What is a quadrilateral with four equal sides and four right angles called?
A) Rectangle
B) Rhombus
C) Square
D) Parallelogram
44. If two lines intersect, the angles opposite each other at the intersection point are called:
A) Adjacent angles
B) Alternate interior angles
C) Vertically opposite angles
D) Corresponding angles
45. What is the sum of angles around a point?
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees
46. What is the area of a triangle with base 'b' and height 'h'?
A) b * h
B) 0.5 * b + h
C) 0.5 * b * h
D) b + h
47. Which theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?
A) Thales's Theorem
B) Pythagorean Theorem
C) Euclid's Theorem
D) Ceva's Theorem
48. What is the property of an equilateral triangle?
A) All angles are different
B) Two angles are equal
C) All sides are different
D) All sides and all angles are equal
49. In a triangle, if two sides are equal, what type of triangle is it called?
A) Scalene triangle
B) Isosceles triangle
C) Equilateral triangle
D) Right-angled triangle
50. What is the sum of the interior angles of a triangle?
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees
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