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## Class 10 Maths Chapter 6 Triangles Important Question Answers

Board | CBSE Board, UP Board, JAC Board, Bihar Board, HBSE Board, UBSE Board, PSEB Board, RBSE Board, JK Board |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Triangles |

Post Type | Study Material |

Medium | Hindi/English |

## Class 10 Maths Chapter 6 Triangles Important Questions

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.

## Class 10 Maths Chapter 6 Triangles One Word Question Answers

**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.

## Class 10 Maths Chapter 6 Triangles Fill In The Blank

**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

**1. In similar triangles, the ratio of corresponding sides is:**

A) Equal

B) Proportional

C) Reciprocal

D) Random

Answer: B) Proportional

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

**2. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of:**

A) Base and perpendicular

B) Two equal sides

C) All three sides

D) Hypotenuse and base

Answer: A) Base and perpendicular

Explanation: This is the Pythagorean theorem, applicable to right triangles.

**3. A triangle with all three sides equal is called:**

A) Isosceles

B) Scalene

C) Equilateral

D) Right-angled

Answer: C) Equilateral

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

**4. The sum of all angles in any triangle is:**

A) 90°

B) 180°

C) 270°

D) 360°

Answer: B) 180°

Explanation: By the angle-sum property, the total of the angles in a triangle is 180°.

**5. If two triangles are similar, then their areas are in the ratio of the square of their:**

A) Perimeters

B) Heights

C) Sides

D) Angles

Answer: C) Sides

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

**6. Two triangles are congruent if they have the same:**

A) Size

B) Shape

C) Both size and shape

D) Angles only

Answer: C) Both size and shape

Explanation: Congruent triangles are identical in both size and shape.

**7. The line segment joining a vertex to the midpoint of the opposite side is called:**

A) Altitude

B) Median

C) Perpendicular

D) Angle bisector

Answer: B) Median

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

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