Geometry MCQs 2026

45 questions with detailed answers · 17 from past papers · 5 quiz batches available

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Read each question, think about the answer, then click Show Answer to reveal the correct option and explanation. Load 10 at a time so it stays manageable — perfect for one-topic study sessions on the bus or during a break.

Page 1 of 1 Questions 1–10 of 45

Q1 medium

The slope of a line joining points (x1,y1) and (x2,y2) is given by
1. A (y2-y1)/(x2-x1)
2. B (x2-x1)/(y2-y1)
3. C (y2+y1)/(x2+x1)
4. D (x2-x1)(y2-y1)
💡 Explanation:
Slope = (y2-y1)/(x2-x1).
Q2 medium

Find the distance between the points (0,0) and (3,4)
1. A 3
2. B 4
3. C 5
4. D 7
💡 Explanation:
Distance = sqrt(3^2+4^2) = sqrt(25) = 5.
Q3 medium

The midpoint of the line segment joining (2,3) and (6,7) is
1. A (3,4)
2. B (5,6)
3. C (2,5)
4. D (4,5)
💡 Explanation:
Midpoint = ((2+6)/2, (3+7)/2) = (4,5).
Q4 Past Paper · PPSC/FPSC/NTS medium

Find the slope of the line joining points (1,2) and (4,8)
1. A 3
2. B 2
3. C 1
4. D 4
💡 Explanation:
Slope = (8-2)/(4-1) = 6/3 = 2.
Q5 hard

Two lines are parallel if their slopes are
1. A negative reciprocals
2. B reciprocals
3. C equal
4. D opposite in sign
💡 Explanation:
Parallel lines have equal slopes.
Q6 hard

Two lines are perpendicular if the product of their slopes equals
1. A 0
2. B 1
3. C undefined
4. D -1
💡 Explanation:
Perpendicular lines have slopes whose product is -1.
Q7 hard

According to the Tangent-Chord angle theorem, the angle between a tangent and a chord equals the angle in the ______ segment
1. A same
2. B major
3. C minor
4. D alternate
💡 Explanation:
By the tangent-chord angle theorem, the angle between a tangent and a chord equals the angle in the alternate segment.
Q8 medium

The tangent to a circle is always
1. A perpendicular to the radius at the point of contact
2. B parallel to the radius
3. C equal to the radius
4. D equal to the diameter
💡 Explanation:
A tangent is always perpendicular to the radius at the point of contact.
Q9 Past Paper · PPSC/FPSC/NTS easy

The longest chord of a circle is its
1. A radius
2. B tangent
3. C secant
4. D diameter
💡 Explanation:
The diameter is the longest chord of a circle, passing through the center.
Q10 easy

A line segment joining two points on a circle is called a
1. A radius
2. B tangent
3. C chord
4. D arc
💡 Explanation:
A chord is a line segment joining two points on a circle.
Q11 Past Paper · PPSC/FPSC/NTS easy

A line that touches a circle at exactly one point is called a
1. A secant
2. B tangent
3. C chord
4. D diameter
💡 Explanation:
A tangent touches a circle at exactly one point.
Q12 medium

Find each exterior angle of a regular octagon
1. A 45°
2. B 40°
3. C 60°
4. D 50°
💡 Explanation:
Each exterior angle = 360/8 = 45 degrees for a regular octagon.
Q13 medium

Each exterior angle of a regular polygon with n sides measures
1. A (n-2)×180/n
2. B 180/n
3. C 360×n
4. D 360/n
💡 Explanation:
Each exterior angle of a regular n-sided polygon is 360/n degrees.
Q14 easy

The sum of angles around a point is
1. A 360°
2. B 180°
3. C 90°
4. D 270°
💡 Explanation:
The angles around a point add up to 360 degrees.
Q15 easy

Angles on a straight line add up to
1. A 90°
2. B 270°
3. C 360°
4. D 180°
💡 Explanation:
Angles on a straight line add up to 180 degrees.
Q16 Past Paper · PPSC/FPSC/NTS easy

Vertically opposite angles formed by two intersecting lines are always
1. A supplementary
2. B complementary
3. C equal
4. D right angles
💡 Explanation:
Vertically opposite angles formed by two intersecting lines are always equal.
Q17 easy

Two angles are called supplementary if their sum equals
1. A 90°
2. B 180°
3. C 270°
4. D 360°
💡 Explanation:
Two angles are supplementary when their measures add up to 180 degrees.
Q18 Past Paper · PPSC/FPSC/NTS easy

Two angles are called complementary if their sum equals
1. A 90°
2. B 180°
3. C 360°
4. D 45°
💡 Explanation:
Two angles are complementary when their measures add up to 90 degrees.
Q19 medium

Each interior angle of a regular pentagon measures
1. A 100°
2. B 120°
3. C 108°
4. D 90°
💡 Explanation:
Each interior angle = 540/5 = 108 degrees for a regular pentagon.
Q20 medium

Find the sum of the interior angles of a hexagon
1. A 540°
2. B 720°
3. C 900°
4. D 1080°
💡 Explanation:
Sum = (6-2) x 180 = 720 degrees for a hexagon.
Q21 Past Paper · PPSC/FPSC/NTS medium

The sum of the interior angles of a polygon with n sides is
1. A (n-2)×180°
2. B (n-1)×180°
3. C n×180°
4. D (n+2)×180°
💡 Explanation:
The sum of interior angles of an n-sided polygon is (n-2) x 180 degrees.
Q22 Past Paper · PPSC/FPSC/NTS easy

The sum of the interior angles of a quadrilateral is
1. A 180°
2. B 270°
3. C 450°
4. D 360°
💡 Explanation:
The interior angles of any quadrilateral sum to 360 degrees.
Q23 medium

If two similar triangles have a scale factor of 3, the ratio of their areas is
1. A 3:1
2. B 6:1
3. C 9:1
4. D 27:1
💡 Explanation:
The ratio of areas of similar triangles equals the square of the scale factor: 3^2 = 9.
Q24 medium

Two triangles are similar if their corresponding
1. A sides are equal
2. B angles are equal
3. C areas are equal
4. D perimeters are equal
💡 Explanation:
Similar triangles have equal corresponding angles and proportional sides.
Q25 medium

The congruence criterion applicable specifically to right triangles is
1. A RHS (right angle-hypotenuse-side)
2. B SSS
3. C ASA
4. D AAA
💡 Explanation:
The RHS criterion (right angle-hypotenuse-side) applies specifically to right triangles.
Q26 Past Paper · PPSC/FPSC/NTS medium

Two triangles are congruent by the SAS criterion if
1. A all three sides are equal
2. B all three angles are equal
3. C two angles and a side are equal
4. D two sides and the included angle are equal
💡 Explanation:
The SAS criterion requires two sides and the included angle to be equal.
Q27 Past Paper · PPSC/FPSC/NTS medium

Two triangles are congruent by the SSS criterion if
1. A two sides and the included angle are equal
2. B two angles and a side are equal
3. C all three corresponding sides are equal
4. D one side and the hypotenuse are equal
💡 Explanation:
The SSS congruence criterion requires all three corresponding sides to be equal.
Q28 medium

If two angles of a triangle are 50° and 70°, find the third angle
1. A 50°
2. B 60°
3. C 70°
4. D 80°
💡 Explanation:
Third angle = 180 - 50 - 70 = 60 degrees.
Q29 Past Paper · PPSC/FPSC/NTS medium

The exterior angle of a triangle equals the
1. A sum of the two non-adjacent interior angles
2. B sum of all three interior angles
3. C half of the opposite interior angle
4. D adjacent interior angle
💡 Explanation:
The exterior angle theorem states the exterior angle equals the sum of the two non-adjacent (remote) interior angles.
Q30 medium

A right triangle has a hypotenuse of 13 and one leg of 5. Find the other leg
1. A 10
2. B 11
3. C 9
4. D 12
💡 Explanation:
Other leg = sqrt(13^2 - 5^2) = sqrt(144) = 12.
Q31 Past Paper · PPSC/FPSC/NTS medium

A right triangle has legs of length 3 and 4. Find the hypotenuse
1. A 6
2. B 4
3. C 5
4. D 7
💡 Explanation:
Hypotenuse = sqrt(3^2 + 4^2) = sqrt(25) = 5.
Q32 Past Paper · PPSC/FPSC/NTS medium

According to the Pythagorean theorem, for a right triangle with legs a, b and hypotenuse c
1. A a+b=c
2. B a^2+b^2=c^2
3. C a^2-b^2=c^2
4. D a+b^2=c^2
💡 Explanation:
The Pythagorean theorem states a^2 + b^2 = c^2 for a right triangle with legs a, b and hypotenuse c.
Q33 easy

In a right triangle, the side opposite the right angle is called the
1. A hypotenuse
2. B base
3. C perpendicular
4. D altitude
💡 Explanation:
The side opposite the right angle in a right triangle is called the hypotenuse.
Q34 easy

A triangle in which one angle equals 90° is called
1. A acute
2. B obtuse
3. C equilateral
4. D right-angled
💡 Explanation:
A right-angled triangle has one angle equal to 90 degrees.
Q35 easy

A triangle with no equal sides is called
1. A equilateral
2. B isosceles
3. C scalene
4. D acute
💡 Explanation:
A scalene triangle has no equal sides.
Q36 easy

A triangle with exactly two equal sides is called
1. A equilateral
2. B isosceles
3. C scalene
4. D obtuse
💡 Explanation:
An isosceles triangle has exactly two equal sides.
Q37 Past Paper · PPSC/FPSC/NTS easy

A triangle with all three sides equal is called
1. A equilateral
2. B isosceles
3. C scalene
4. D right-angled
💡 Explanation:
An equilateral triangle has all three sides (and angles) equal.
Q38 medium

If two parallel lines are cut by a transversal, co-interior (allied) angles are
1. A equal
2. B complementary
3. C vertically opposite
4. D supplementary
💡 Explanation:
Co-interior (allied) angles formed by a transversal with parallel lines are supplementary.
Q39 medium

If two parallel lines are cut by a transversal, alternate interior angles are
1. A supplementary
2. B complementary
3. C equal
4. D right angles
💡 Explanation:
When a transversal cuts two parallel lines, alternate interior angles are equal.
Q40 Past Paper · PPSC/FPSC/NTS easy

The sum of the interior angles of a triangle is
1. A 90°
2. B 180°
3. C 270°
4. D 360°
💡 Explanation:
The three interior angles of any triangle always add up to 180 degrees.
Q41 Past Paper · PPSC/FPSC/NTS medium

The distance between two points (x1,y1) and (x2,y2) is given by
1. A (x2-x1)+(y2-y1)
2. B sqrt((x2-x1)^2+(y2-y1)^2)
3. C (x2-x1)^2+(y2-y1)^2
4. D sqrt((x2-x1)+(y2-y1))
💡 Explanation:
The distance formula is sqrt((x2-x1)^2 + (y2-y1)^2).
Q42 medium

The perpendicular drawn from the center of a circle to a chord
1. A bisects the chord
2. B doubles the chord
3. C trisects the chord
4. D is parallel to the chord
💡 Explanation:
A perpendicular from the center of a circle to a chord bisects that chord.
Q43 medium

Equal chords of a circle subtend ______ angles at the center
1. A supplementary
2. B complementary
3. C different
4. D equal
💡 Explanation:
Equal chords subtend equal angles at the center of a circle.
Q44 Past Paper · PPSC/FPSC/NTS hard

The angle subtended by an arc at the center of a circle is ______ the angle subtended by it at any point on the remaining part of the circle
1. A equal to
2. B half of
3. C twice
4. D three times
💡 Explanation:
The angle at the center is twice the angle subtended at the circumference by the same arc.
Q45 Past Paper · PPSC/FPSC/NTS medium

The angle in a semicircle is
1. A 45°
2. B 90°
3. C 180°
4. D 60°
💡 Explanation:
Any angle inscribed in a semicircle is a right angle (90 degrees).

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Geometry MCQs 2026

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