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 1Questions 1–10 of 45

Q1hard
Two lines are parallel if their slopes are
1. Anegative reciprocals
2. Breciprocals
3. Cequal
4. Dopposite in sign
💡 Explanation:
Parallel lines have equal slopes.
Q2Past Paper · PPSC/FPSC/NTSmedium
Find the slope of the line joining points (1,2) and (4,8)
1. A3
2. B2
3. C1
4. D4
💡 Explanation:
Slope = (8-2)/(4-1) = 6/3 = 2.
Q3medium
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).
Q4medium
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).
Q5medium
Find the distance between the points (0,0) and (3,4)
1. A3
2. B4
3. C5
4. D7
💡 Explanation:
Distance = sqrt(3^2+4^2) = sqrt(25) = 5.
Q6hard
According to the Tangent-Chord angle theorem, the angle between a tangent and a chord equals the angle in the ______ segment
1. Asame
2. Bmajor
3. Cminor
4. Dalternate
💡 Explanation:
By the tangent-chord angle theorem, the angle between a tangent and a chord equals the angle in the alternate segment.
Q7hard
Two lines are perpendicular if the product of their slopes equals
1. A0
2. B1
3. Cundefined
4. D-1
💡 Explanation:
Perpendicular lines have slopes whose product is -1.
Q8Past Paper · PPSC/FPSC/NTSmedium
The distance between two points (x1,y1) and (x2,y2) is given by
1. A(x2-x1)+(y2-y1)
2. Bsqrt((x2-x1)^2+(y2-y1)^2)
3. C(x2-x1)^2+(y2-y1)^2
4. Dsqrt((x2-x1)+(y2-y1))
💡 Explanation:
The distance formula is sqrt((x2-x1)^2 + (y2-y1)^2).
Q9easy
In a right triangle, the side opposite the right angle is called the
1. Ahypotenuse
2. Bbase
3. Cperpendicular
4. Daltitude
💡 Explanation:
The side opposite the right angle in a right triangle is called the hypotenuse.
Q10Past Paper · PPSC/FPSC/NTSmedium
According to the Pythagorean theorem, for a right triangle with legs a, b and hypotenuse c
1. Aa+b=c
2. Ba^2+b^2=c^2
3. Ca^2-b^2=c^2
4. Da+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.
Q11easy
A triangle with no equal sides is called
1. Aequilateral
2. Bisosceles
3. Cscalene
4. Dacute
💡 Explanation:
A scalene triangle has no equal sides.
Q12easy
A triangle with exactly two equal sides is called
1. Aequilateral
2. Bisosceles
3. Cscalene
4. Dobtuse
💡 Explanation:
An isosceles triangle has exactly two equal sides.
Q13Past Paper · PPSC/FPSC/NTSeasy
A triangle with all three sides equal is called
1. Aequilateral
2. Bisosceles
3. Cscalene
4. Dright-angled
💡 Explanation:
An equilateral triangle has all three sides (and angles) equal.
Q14medium
If two parallel lines are cut by a transversal, co-interior (allied) angles are
1. Aequal
2. Bcomplementary
3. Cvertically opposite
4. Dsupplementary
💡 Explanation:
Co-interior (allied) angles formed by a transversal with parallel lines are supplementary.
Q15medium
If two parallel lines are cut by a transversal, alternate interior angles are
1. Asupplementary
2. Bcomplementary
3. Cequal
4. Dright angles
💡 Explanation:
When a transversal cuts two parallel lines, alternate interior angles are equal.
Q16Past Paper · PPSC/FPSC/NTSeasy
The sum of the interior angles of a triangle is
1. A90°
2. B180°
3. C270°
4. D360°
💡 Explanation:
The three interior angles of any triangle always add up to 180 degrees.
Q17easy
The sum of angles around a point is
1. A360°
2. B180°
3. C90°
4. D270°
💡 Explanation:
The angles around a point add up to 360 degrees.
Q18easy
Angles on a straight line add up to
1. A90°
2. B270°
3. C360°
4. D180°
💡 Explanation:
Angles on a straight line add up to 180 degrees.
Q19Past Paper · PPSC/FPSC/NTSeasy
Vertically opposite angles formed by two intersecting lines are always
1. Asupplementary
2. Bcomplementary
3. Cequal
4. Dright angles
💡 Explanation:
Vertically opposite angles formed by two intersecting lines are always equal.
Q20easy
Two angles are called supplementary if their sum equals
1. A90°
2. B180°
3. C270°
4. D360°
💡 Explanation:
Two angles are supplementary when their measures add up to 180 degrees.
Q21Past Paper · PPSC/FPSC/NTSeasy
Two angles are called complementary if their sum equals
1. A90°
2. B180°
3. C360°
4. D45°
💡 Explanation:
Two angles are complementary when their measures add up to 90 degrees.
Q22easy
A triangle in which one angle equals 90° is called
1. Aacute
2. Bobtuse
3. Cequilateral
4. Dright-angled
💡 Explanation:
A right-angled triangle has one angle equal to 90 degrees.
Q23Past Paper · PPSC/FPSC/NTSmedium
A right triangle has legs of length 3 and 4. Find the hypotenuse
1. A6
2. B4
3. C5
4. D7
💡 Explanation:
Hypotenuse = sqrt(3^2 + 4^2) = sqrt(25) = 5.
Q24medium
A right triangle has a hypotenuse of 13 and one leg of 5. Find the other leg
1. A10
2. B11
3. C9
4. D12
💡 Explanation:
Other leg = sqrt(13^2 - 5^2) = sqrt(144) = 12.
Q25Past Paper · PPSC/FPSC/NTSmedium
The exterior angle of a triangle equals the
1. Asum of the two non-adjacent interior angles
2. Bsum of all three interior angles
3. Chalf of the opposite interior angle
4. Dadjacent interior angle
💡 Explanation:
The exterior angle theorem states the exterior angle equals the sum of the two non-adjacent (remote) interior angles.
Q26medium
If two angles of a triangle are 50° and 70°, find the third angle
1. A50°
2. B60°
3. C70°
4. D80°
💡 Explanation:
Third angle = 180 - 50 - 70 = 60 degrees.
Q27Past Paper · PPSC/FPSC/NTSmedium
Two triangles are congruent by the SSS criterion if
1. Atwo sides and the included angle are equal
2. Btwo angles and a side are equal
3. Call three corresponding sides are equal
4. Done side and the hypotenuse are equal
💡 Explanation:
The SSS congruence criterion requires all three corresponding sides to be equal.
Q28Past Paper · PPSC/FPSC/NTSmedium
Two triangles are congruent by the SAS criterion if
1. Aall three sides are equal
2. Ball three angles are equal
3. Ctwo angles and a side are equal
4. Dtwo sides and the included angle are equal
💡 Explanation:
The SAS criterion requires two sides and the included angle to be equal.
Q29medium
The congruence criterion applicable specifically to right triangles is
1. ARHS (right angle-hypotenuse-side)
2. BSSS
3. CASA
4. DAAA
💡 Explanation:
The RHS criterion (right angle-hypotenuse-side) applies specifically to right triangles.
Q30medium
Two triangles are similar if their corresponding
1. Asides are equal
2. Bangles are equal
3. Careas are equal
4. Dperimeters are equal
💡 Explanation:
Similar triangles have equal corresponding angles and proportional sides.
Q31medium
If two similar triangles have a scale factor of 3, the ratio of their areas is
1. A3:1
2. B6:1
3. C9:1
4. D27:1
💡 Explanation:
The ratio of areas of similar triangles equals the square of the scale factor: 3^2 = 9.
Q32Past Paper · PPSC/FPSC/NTSeasy
The sum of the interior angles of a quadrilateral is
1. A180°
2. B270°
3. C450°
4. D360°
💡 Explanation:
The interior angles of any quadrilateral sum to 360 degrees.
Q33Past Paper · PPSC/FPSC/NTSmedium
The sum of the interior angles of a polygon with n sides is
1. A(n-2)×180°
2. B(n-1)×180°
3. Cn×180°
4. D(n+2)×180°
💡 Explanation:
The sum of interior angles of an n-sided polygon is (n-2) x 180 degrees.
Q34medium
Find the sum of the interior angles of a hexagon
1. A540°
2. B720°
3. C900°
4. D1080°
💡 Explanation:
Sum = (6-2) x 180 = 720 degrees for a hexagon.
Q35medium
Each interior angle of a regular pentagon measures
1. A100°
2. B120°
3. C108°
4. D90°
💡 Explanation:
Each interior angle = 540/5 = 108 degrees for a regular pentagon.
Q36medium
Each exterior angle of a regular polygon with n sides measures
1. A(n-2)×180/n
2. B180/n
3. C360×n
4. D360/n
💡 Explanation:
Each exterior angle of a regular n-sided polygon is 360/n degrees.
Q37medium
Find each exterior angle of a regular octagon
1. A45°
2. B40°
3. C60°
4. D50°
💡 Explanation:
Each exterior angle = 360/8 = 45 degrees for a regular octagon.
Q38Past Paper · PPSC/FPSC/NTSeasy
A line that touches a circle at exactly one point is called a
1. Asecant
2. Btangent
3. Cchord
4. Ddiameter
💡 Explanation:
A tangent touches a circle at exactly one point.
Q39easy
A line segment joining two points on a circle is called a
1. Aradius
2. Btangent
3. Cchord
4. Darc
💡 Explanation:
A chord is a line segment joining two points on a circle.
Q40Past Paper · PPSC/FPSC/NTSeasy
The longest chord of a circle is its
1. Aradius
2. Btangent
3. Csecant
4. Ddiameter
💡 Explanation:
The diameter is the longest chord of a circle, passing through the center.
Q41medium
The tangent to a circle is always
1. Aperpendicular to the radius at the point of contact
2. Bparallel to the radius
3. Cequal to the radius
4. Dequal to the diameter
💡 Explanation:
A tangent is always perpendicular to the radius at the point of contact.
Q42Past Paper · PPSC/FPSC/NTSmedium
The angle in a semicircle is
1. A45°
2. B90°
3. C180°
4. D60°
💡 Explanation:
Any angle inscribed in a semicircle is a right angle (90 degrees).
Q43Past Paper · PPSC/FPSC/NTShard
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. Aequal to
2. Bhalf of
3. Ctwice
4. Dthree times
💡 Explanation:
The angle at the center is twice the angle subtended at the circumference by the same arc.
Q44medium
Equal chords of a circle subtend ______ angles at the center
1. Asupplementary
2. Bcomplementary
3. Cdifferent
4. Dequal
💡 Explanation:
Equal chords subtend equal angles at the center of a circle.
Q45medium
The perpendicular drawn from the center of a circle to a chord
1. Abisects the chord
2. Bdoubles the chord
3. Ctrisects the chord
4. Dis parallel to the chord
💡 Explanation:
A perpendicular from the center of a circle to a chord bisects that chord.

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Geometry MCQs 2026

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