Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Very Short Answer Type Questions: Triangles
Class 9 Maths Question Answers - Triangles
Q.1. In a ΔABC, BC = CA and ∠ A = 50°, which is longer BC or AB?
Sol. ∵ ∠ 1 = ∠ 2 [∵ AC = BC]
and ∠A = ∠1 = 50°
⇒ ∠ 2 = 50°
⇒ ∠1+ ∠2+ ∠3= 180 [ angle sum property ]
∴ ∠ C = 180º - [50° + 50°] = 80°
⇒ Since, ∠C > ∠A
⇒ AB > BC Thus, AB is greater. [The greatest side is opp. to the greatest angle.]
Q.2. In ΔABC, ∠ B = 60° and ∠ C = 63°. Name the greatest side.
Sol. In ΔABC, ∠ B = 60° and ∠ C = 63°
⇒ ∠A+ ∠B+ ∠C= 180 [ angle sum property ]
⇒ ∠ A = 180º - (60° + 63°) = 57°
⇒ The greatest side is opp. to the greatest angle, i.e., 63°
∴ Side AB is the greatest.
Q.3. In ΔABC, if BC = AB and ∠ B = 80°, then find the measure of∠ A.
Sol. BC = AB ⇒ ∠A = ∠C
⇒ ∠A+ ∠B+ ∠C= 180 [ angle sum property ]
∵ ∠B = 80°
∴ ∠A + ∠C = 180° - 80° = 100°
⇒ ∠A = ∠C = 50º
Q.4. Which of the following is not the criterion for congruence of triangles?
(i) SAS (ii) SSA (iii) ASA (iv) RHS
Ans: SSA is not the criterion for congruency.
Q.5. If two angles are (30 - a)º and (125 + 2a)º and they are supplement of each other. Find the value of ‘a’.
Sol. ∵ (30 - a)º and (125 + 2a)º are supplement to each other.
∴ (30 - a + 125 + 2a)º = 180º
⇒ a = 180º - 125º - 30º = 25º
⇒ Value of a = 25°
Q.6. Each of the equal angles of an isosceles triangle is 38°. What is the measure of the third angle?
Sol. Let the third angle = x
∴ x + 38° + 38° = 180°
⇒ x = 180° - 38° - 38° = 104º
Q.7. In an isosceles ΔABC, AB = AC and ∠ A= 80°. What is the measure of ∠ B?
Sol. We have AB = AC ⇒ ∠ B = ∠ C [∵ Angles opposite to equal sides are equal]
∴ ∠A + ∠B + ∠C = 180°
⇒ ∠A + ∠B + ∠B = 180°
⇒ ∠A + 2∠B = 180°
⇒ 80° + 2∠B = 180°
⇒ 2∠B = 180°- 80°
= 100
⇒ ∠B= (100o/2) = 50°
Q.8. Find the measure of each acute angle in a right angle isosceles triangle.
Sol. Let the measure of each of the equal acute angle of the Δ be x
∴ We have: x + x + 90° = 180°
⇒ x + x = 180° - 90° = 90°
⇒ x= (90o/2)= 45°
The document Class 9 Maths Question Answers - Triangles is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Question Answers - Triangles
| 1. What are the properties of triangles? |  |
Ans. The properties of triangles include the sum of the interior angles being 180 degrees, the relationship between the lengths of sides (Triangle Inequality Theorem), and the classification into different types (scalene, isosceles, and equilateral) based on side lengths and angles.
| 2. How do you calculate the area of a triangle? | |
Ans. The area of a triangle can be calculated using the formula: Area = (1/2) × base × height. Alternatively, if the side lengths are known, Heron's formula can be used: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter, and a, b, c are the side lengths.
| 3. What is the difference between acute, obtuse, and right triangles? | |
Ans. An acute triangle has all angles less than 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and a right triangle has one angle exactly equal to 90 degrees.
| 4. How can you determine if three lengths can form a triangle? | |
Ans. To determine if three lengths can form a triangle, use the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third side for all three combinations.
| 5. What are congruent triangles and how can they be proven? | |
Ans. Congruent triangles are triangles that are identical in shape and size. They can be proven congruent using various criteria, such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS) congruence.
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