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Triangles Quiz - CBSE Class 8 Mathematics

Free practice quiz: Triangles (CBSE Class 8 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 16 multiple-choice questions on Triangles, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Types of triangles

By sides: a scalene triangle has all sides different, isosceles has two equal sides, and equilateral has all three equal.
By angles: an acute triangle has all angles acute, a right triangle has one right angle, and an obtuse triangle has one obtuse angle.
Isosceles: the angles opposite the equal sides are equal. Equilateral: all angles are equal, each one-third of 180°.

Isosceles property

\[AB = AC \Rightarrow \angle B = \angle C\]

Equilateral angles

\[\angle A = \angle B = \angle C = \frac{180^\circ}{3}\]

Common mistake: Thinking an equilateral triangle cannot be isosceles. It is a special isosceles triangle because it has at least two equal sides.

Angle sum property

The three interior angles of any triangle always add up to 180°.
If two angles are known, subtract their sum from 180° to find the third angle.
An exterior angle equals the sum of the two interior opposite angles.

Angle sum

\[\angle A + \angle B + \angle C = 180^\circ\]

Third angle

\[\angle C = 180^\circ - (\angle A + \angle B)\]

Exterior angle at C

\[\angle ACD = \angle A + \angle B\]

Common mistake: Subtracting only one known angle from 180°, or using 360° as the angle sum of a triangle instead of 180°.

Perimeter and area

Perimeter is the total length of all three sides added together.
Area is half of base times height. The height is perpendicular to that chosen base.
To find the height from the area, double the area and divide by the base on which that height stands.

Perimeter

\[P = a + b + c\]

Missing side from perimeter

\[c = P - (a + b)\]

Area (b = base, h = height to that base)

\[A = \frac{1}{2} \times b \times h\]

Height from area (b = base matching h)

\[h = \frac{2A}{b}\]

Common mistake: Using a slanted side as the height, or forgetting the one-half in the area formula.

Pythagoras theorem and converse

In a right triangle, the hypotenuse is the longest side. It lies opposite the right angle.
The square of the hypotenuse c equals the sum of the squares of the two legs a and b.
Converse: let c be the longest side. If a² + b² = c², the triangle is right-angled.

Theorem (c = hypotenuse)

\[c^2 = a^2 + b^2\]

Hypotenuse from legs a, b

\[c = \sqrt{a^2 + b^2}\]

Missing leg (c = hypotenuse, b = other leg)

\[a = \sqrt{c^2 - b^2}\]

Converse (c = longest side)

\[a^2 + b^2 = c^2 \Rightarrow \text{right angle opposite } c\]

Common mistake: Testing the converse with a shorter side as c, or finding a leg using c² + b² instead of c² − b².

Enrichment: incircle and circumcircle radii

This goes beyond the NCERT syllabus. The circumcircle passes through all three vertices. The incircle touches all three sides from inside.
Semi-perimeter s is half the perimeter. The inradius r equals the area divided by s.
In an equilateral triangle with side a, the circumradius R is twice the inradius r.

Semi-perimeter

\[s = \frac{a + b + c}{2}\]

Inradius of any triangle (A = area)

\[r = \frac{A}{s}\]

Circumradius of equilateral triangle

\[R = \frac{a}{\sqrt{3}}\]

Inradius of equilateral triangle

\[r = \frac{a}{2\sqrt{3}}\]

Common mistake: Dividing the area by the full perimeter instead of the semi-perimeter, or mixing up the circumradius R with the inradius r.

Exam tips

Before using Pythagoras, find the longest side first. That side must be c.
For a side ratio, test the largest term as c. Multiplying all sides by the same number keeps the triangle's type.
Always write units: lengths in cm and area in cm².

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the sum of the interior angles of a triangle?
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Answer: B. 180 degrees
The sum of the interior angles of a triangle is always 180 degrees regardless of the type of triangle.
A triangle has angles measuring 50° and 60°. What is the measure of the third angle?
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Answer: A. 70°
The sum of angles in a triangle is always 180°. Therefore, the third angle = 180° - (50° + 60°) = 70°.
A triangle has sides measuring 3 cm, 4 cm, and 5 cm. What type of triangle is it?
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Answer: C. Right triangle
This triangle satisfies the Pythagorean theorem: 3² + 4² = 9 + 16 = 25 = 5², so it is a right triangle.
In an equilateral triangle, if one angle measures 60°, what are the measures of the other two angles?
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Answer: A. 60° each
An equilateral triangle has all angles equal, hence if one angle is 60°, the other two angles are also 60°.
If the area of a triangle is 24 cm² and its base is 8 cm, what is its height?
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Answer: C. 6 cm
Using the area formula: Area = 1/2 × base × height, we can find the height. Thus, 24 = 1/2 × 8 × height, which means height = 6 cm.