Class 10 Maths Chapter 6 Triangles Important Question Answers

Question 1: State and prove the Basic Proportionality Theorem (BPT).

Question 2: If ΔABC ∼ ΔDEF and their areas are 144 cm² and 81 cm², find the ratio of their corresponding sides.

Question 3: In a triangle, a line parallel to one side divides the other two sides proportionally. Prove this theorem.

Question 4: In ΔPQR, PS is a median and also an altitude. Prove that ΔPQR is an isosceles triangle.

Question 5: If in ΔABC, DE || BC and AD/DB = 3/4, find the ratio of the areas of ΔADE and ΔABC.

Question 6: Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Question 7: In an equilateral triangle, prove that the centroid, circumcenter, and orthocenter coincide.

Question 8: If ΔABC ∼ ΔPQR, prove that AB/AC = PQ/PR.

Question 9: In ΔABC, if ∠A = 90° and AB = AC, prove that ΔABC is an isosceles right triangle.

Question 10: Prove that the diagonals of a rhombus bisect each other at right angles.

1. What is the ratio of corresponding sides in similar triangles?

Answer: Proportion

Explanation: In similar triangles, corresponding sides are in proportion.

2. What type of angle do the altitudes of an equilateral triangle form at each vertex?

Answer: Right

Explanation: The altitudes of an equilateral triangle form a 90-degree angle at each vertex.

3. In a right triangle, which formula is used to relate the lengths of sides?

Answer: Pythagoras

Explanation: The Pythagorean theorem relates the squares of the sides in a right triangle.

4. What is the name of the largest side in a right triangle?

Answer: Hypotenuse

Explanation: The side opposite the right angle is called the hypotenuse, the longest side.

5. What term describes triangles with all sides and angles equal?

Answer: Equilateral

Explanation: An equilateral triangle has all three sides and angles equal.

6. Which property states that the sum of angles in any triangle is 180 degrees?

Answer: Angle-Sum

Explanation: The angle-sum property of a triangle states that interior angles add up to 180 degrees.

7. What is the common name for triangles with one angle greater than 90 degrees?

Answer: Obtuse

Explanation: An obtuse triangle has one angle that is greater than 90 degrees.

8. Which line segment in a triangle joins a vertex to the midpoint of the opposite side?

Answer: Median

Explanation: A median connects a vertex to the midpoint of the opposite side.

9. In a triangle, what is the line segment that is perpendicular to a side and passes through the opposite vertex?

Answer: Altitude

Explanation: An altitude is perpendicular from a vertex to the opposite side.

10. What is the criterion for similarity involving two pairs of equal angles?

Answer: AA (Angle-Angle)

Explanation: AA similarity criterion states that two triangles are similar if two angles are equal.

11. What type of triangle has two equal sides and two equal angles?

Answer: Isosceles

Explanation: An isosceles triangle has two sides of equal length and two equal angles.

12. Which theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides?

Answer: Pythagorean

Explanation: The Pythagorean theorem applies to right triangles and relates the hypotenuse to other sides.

13. Which ratio in a right triangle is defined as opposite side divided by hypotenuse?

Answer: Sine

Explanation: The sine of an angle is the ratio of the opposite side to the hypotenuse.

14. What is the point where all three medians of a triangle intersect called?

Answer: Centroid

Explanation: The centroid is the point of intersection of the three medians in a triangle.

15. In a right triangle, the ratio of adjacent side to hypotenuse is known as?

Answer: Cosine

Explanation: Cosine of an angle is the ratio of the adjacent side to the hypotenuse.

1. In similar triangles, the ratio of corresponding sides is always ______.

Answer: Proportional

Explanation: Similar triangles have corresponding sides in proportion.

2. The longest side of a right triangle is called the ______.

Answer: Hypotenuse

Explanation: In a right triangle, the hypotenuse is the side opposite the right angle.

3. A triangle with all three sides equal is called an ______ triangle.

Answer: Equilateral

Explanation: An equilateral triangle has all three sides of equal length and angles of 60° each.

4. The sum of all angles in a triangle is ______ degrees.

Answer: 180

Explanation: The angle-sum property states that the sum of angles in any triangle is 180°.

5. A triangle with one angle greater than 90° is called an ______ triangle.

Answer: Obtuse

Explanation: An obtuse triangle has one angle greater than 90°.

6. A triangle with one 90° angle is called a ______ triangle.

Answer: Right

Explanation: A right triangle has one angle exactly equal to 90°.

7. The perpendicular distance from a vertex to the opposite side is called the ______.

Answer: Altitude

Explanation: An altitude is drawn from a vertex perpendicular to the opposite side.

8. The line segment joining a vertex to the midpoint of the opposite side is called the ______.

Answer: Median

Explanation: A median connects a vertex to the midpoint of the opposite side in a triangle.

9. In similar triangles, the ratio of the areas is equal to the square of the ratio of their ______.

Answer: Sides

Explanation: Area ratio of similar triangles is the square of the ratio of corresponding sides.

10. Two triangles are similar if their corresponding angles are ______.

Answer: Equal

Class 10 Maths Chapter 6 Triangles Multiple Choice Questions

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