20 Triangle Quiz Questions and Answers

Question 1:
What is the sum of the interior angles of any triangle?
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees

Answer: B) 180 degrees

Explanation: In Euclidean geometry, the interior angles of any triangle always add up to 180 degrees.

Question 2:
Which type of triangle has all sides of equal length?
A) Isosceles
B) Scalene
C) Equilateral
D) Right-angled

Answer: C) Equilateral

Explanation: An equilateral triangle is defined by having all three sides equal in length.

Question 3:
In a right-angled triangle, what is the relationship between the sides a, b, and c (where c is the hypotenuse)?
A) a + b = c
B) a² + b² = c²
C) a × b = c
D) a – b = c

Answer: B) a² + b² = c²

Explanation: This is the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Question 4:
What is the minimum number of sides that must be equal for a triangle to be isosceles?
A) 1
B) 2
C) 3
D) 0

Answer: B) 2

Explanation: An isosceles triangle has at least two sides of equal length.

Question 5:
If a triangle has angles of 30 degrees, 60 degrees, and 90 degrees, what type of triangle is it?
A) Acute
B) Obtuse
C) Right-angled
D) Equilateral

Answer: C) Right-angled

Explanation: A triangle with a 90-degree angle is classified as a right-angled triangle.

Question 6:
Which theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side?
A) Pythagorean theorem
B) Triangle inequality theorem
C) Angle sum theorem
D) Congruence theorem

Answer: B) Triangle inequality theorem

Explanation: The triangle inequality theorem ensures that the sides of a triangle can form a valid triangle.

Question 7:
What is the area of a triangle with base 10 cm and height 5 cm?
A) 15 cm²
B) 25 cm²
C) 50 cm²
D) 20 cm²

Answer: B) 25 cm²

Explanation: The formula for the area of a triangle is (base × height) / 2, so (10 × 5) / 2 = 25 cm².

Question 8:
In an equilateral triangle, what is the measure of each interior angle?
A) 60 degrees
B) 90 degrees
C) 120 degrees
D) 45 degrees

Answer: A) 60 degrees

Explanation: All angles in an equilateral triangle are equal, and since the sum is 180 degrees, each angle is 60 degrees.

Question 9:
Which of the following sets of side lengths can form a triangle?
A) 3, 4, 8
B) 5, 12, 13
C) 2, 2, 5
D) 1, 1, 3

Answer: B) 5, 12, 13

Explanation: Using the triangle inequality theorem, 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5, so these lengths form a triangle.

Question 10:
What type of triangle has one angle greater than 90 degrees?
A) Acute
B) Right-angled
C) Obtuse
D) Isosceles

Answer: C) Obtuse

Explanation: An obtuse triangle is defined by having one angle that measures more than 90 degrees.

Question 11:
If two triangles have all corresponding sides equal, what are they?
A) Similar
B) Congruent
C) Isosceles
D) Scalene

Answer: B) Congruent

Explanation: Congruent triangles have identical shapes and sizes, meaning all corresponding sides and angles are equal.

Question 12:
What is the perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm?
A) 18 cm
B) 24 cm
C) 20 cm
D) 34 cm

Answer: B) 24 cm

Explanation: Perimeter is the sum of all sides: 7 + 8 + 9 = 24 cm.

Question 13:
In a 45-45-90 triangle, what is the ratio of the sides (legs to hypotenuse)?
A) 1:1:√2
B) 1:1:1
C) 1:√3:2
D) 1:2:3

Answer: A) 1:1:√2

Explanation: In an isosceles right-angled triangle, the legs are equal, and the hypotenuse is leg × √2.

Question 14:
Which angle is opposite the longest side in any triangle?
A) The smallest angle
B) The largest angle
C) The median angle
D) Any angle

Answer: B) The largest angle

Explanation: In a triangle, the largest angle is always opposite the longest side.

Question 15:
What is the formula for the area of an equilateral triangle with side length a?
A) (a² × √3) / 4
B) (a × √3) / 2
C) a²
D) (a²) / 2

Answer: A) (a² × √3) / 4

Explanation: The area of an equilateral triangle is calculated using the formula (side² × √3) / 4.

Question 16:
If two triangles are similar, what is true about their sides?
A) All sides are equal
B) Corresponding sides are proportional
C) All angles are equal
D) Both B and C

Answer: D) Both B and C

Explanation: Similar triangles have corresponding angles equal and corresponding sides in proportion.

Question 17:
What type of triangle has sides in the ratio 3:4:5?
A) Acute
B) Obtuse
C) Right-angled
D) Equilateral

Answer: C) Right-angled

Explanation: A 3-4-5 triangle satisfies the Pythagorean theorem (3² + 4² = 9 + 16 = 25 = 5²), making it right-angled.

Question 18:
How many lines of symmetry does an isosceles triangle have?
A) 0
B) 1
C) 2
D) 3

Answer: B) 1

Explanation: An isosceles triangle has one line of symmetry along the altitude from the apex to the base.

Question 19:
In a triangle with sides 5 cm, 5 cm, and 6 cm, what type of triangle is it?
A) Equilateral
B) Isosceles
C) Scalene
D) Right-angled

Answer: B) Isosceles

Explanation: Since two sides are equal (5 cm and 5 cm), it is an isosceles triangle.

Question 20:
What is the exterior angle of a triangle equal to?
A) The sum of the two opposite interior angles
B) Half of the largest interior angle
C) The difference of the two adjacent interior angles
D) 180 degrees minus the interior angle

Answer: A) The sum of the two opposite interior angles

Explanation: An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.