Triangles Quiz - CBSE Class 10 Mathematics
Free practice quiz: Triangles (CBSE Class 10 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 10 Mathematics practice quiz has 11 multiple-choice questions on Triangles, and 11 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.
Start quiz: 11 questions, freeAbout this topic
Two figures with the same shape but not necessarily the same size are similar. For triangles, equal angles and proportional sides go together. Similarity leads to the Basic Proportionality Theorem, area ratios and the Pythagoras theorem.
- Similar triangles: corresponding angles are equal and corresponding sides are in the same ratio.
- BPT (Thales): a line parallel to one side divides the other two sides in the same ratio.
- Converse of BPT: if a line divides two sides in the same ratio, it is parallel to the third side.
- AA criterion: two pairs of equal angles are enough to prove similarity.
- SSS: all three sides proportional. SAS: two sides proportional and the included angles equal.
- Area ratio of similar triangles equals the square of the ratio of corresponding sides.
- Pythagoras: in a right triangle, hypotenuse squared equals the sum of squares of the other two sides. Its converse is also true.
Learn the key ideas Beta
Angle Sum and Triangle Types
- The three angles of any triangle together make two right angles, a straight angle.
- In a right triangle the two non-right angles are complementary. An obtuse triangle has one angle greater than a right angle.
- In an isosceles triangle, the angles opposite the equal sides are equal.
Common mistake: Assuming the given angle in an isosceles triangle is always a base angle. It could be the vertex angle, so check both cases.
Congruence and Side-Angle Rules
- Two triangles are congruent by SSS, SAS, ASA, AAS or RHS. SSA and AAA do not prove congruence.
- The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.
- Any two sides together must be longer than the third side.
Common mistake: Naming the angle at a vertex of the longest side. The largest angle is opposite the longest side, not touching it.
Pythagoras Theorem and Its Converse
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
- If the sides satisfy this relation, the triangle is right-angled, with the right angle opposite the longest side.
Common mistake: Adding the legs directly instead of squaring them first, or forgetting to take the square root at the end.
Area, Height and Equilateral Triangles
- Area is half of base times perpendicular height. Rearrange this to find the height or the base.
- In an equilateral triangle the height bisects the base. Pythagoras then gives the height.
- An equilateral triangle has one line of symmetry through each vertex.
Common mistake: Using a slanted side as the height. The height must be perpendicular to the chosen base.
Centroid, Circumcentre and Incentre
- Medians meet at the centroid. Perpendicular bisectors of the sides meet at the circumcentre.
- The circumcentre is equidistant from all vertices. The incentre, where the angle bisectors meet, is equidistant from all sides.
Common mistake: Mixing up the centres: the centroid comes from medians, the circumcentre from perpendicular bisectors, and the incentre from angle bisectors.
Exam tips
- Draw a rough sketch and mark equal sides and angles before calculating.
- For any three sides, check whether the squares fit Pythagoras before naming the triangle type.
- Write units for every answer: cm for lengths, square cm for area.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
If two sides of a triangle are 8 cm and 15 cm, what could be the length range for the third side?
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Answer: A. Between 7 cm and 23 cm
By the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For this triangle, the possible range for the third side is (15 - 8) < x < (15 + 8), which simplifies to 7 < x < 23.
What is the area of an equilateral triangle with a side length of 4 cm?
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Answer: A. 4√3 cm²
The area of an equilateral triangle is calculated as (√3 / 4) * side². For a side length of 4 cm, the area is (√3 / 4) * 4² = 4√3 cm².
If a triangle has sides 5 cm, 12 cm, and 13 cm, what type of triangle is it?
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Answer: C. Right
This triangle is a right triangle because 5² + 12² = 25 + 144 = 169 = 13², satisfying the Pythagorean theorem.
The medians of a triangle intersect at a single point known as what?
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Answer: B. Centroid
The medians of a triangle intersect at the centroid. It is the balancing point of the triangle.
What is the length of the altitude from the right angle in a triangle with legs 9 cm and 12 cm?
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Answer: B. 7.2 cm
The altitude (h) from the right angle in a right triangle divides the triangle into two smaller triangles that are similar to the original triangle. Using the area method: area = 0.5 * 9 * 12 = 54. For the height (h), 0.5 * hypotenuse (15) * h = 54, thus h = 7.2 cm.
More questions in this quiz
Answers and explanations are in the full quiz.
- What is the hypotenuse of a right triangle with legs of lengths 3 cm and 4 cm?
- How many lines of symmetry does an equilateral triangle have?
- What is the perpendicular height of a triangle with a base of 6 cm and area of 18 cm²?
- What is the relationship between the circumcenter and the vertices of a triangle?
- What is the inscribed circle radius of a triangle with sides 5 cm, 12 cm, and 13 cm?
- How many non-congruent triangles can a scalene triangle have?