## Constructions

*Very Short Questions and Answers*

**Based NCERT Class 9 Mathematics Chapter**

**Q1: With the help of ruler and compass, which of the following angles can be constructed?**

(a) 35°

(b) 40°

(c) 37.5°

(d) 15°

Answer: 37.5° and 15° angles can be constructed using a ruler and a compass.

**Q2(NCERT Exemplar): With the help of a ruler and a compass it is not possible to construct an angle of :**

(A) 37.5°

(B) 40°

(C) 22.5°

(D) 67.5°

Answer: (B) 40°

**Q3 (NCERT Exemplar): Write True or False in each of the following. Give reasons for your answer:**

1. An angle of 52.5° can be constructed.

2. An angle of 42.5° can be constructed.

3. A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.

4. A triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.

5. A triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.

6. A triangle ABC can be constructed in which ∠ B = 60°, ∠C = 45° and AB + BC + AC = 12 cm

Answers:

1: True. Construct 210° (180° + 30°), bisect it two times, 210° ÷ 4 = 52.5°

2: False. Since 85° ÷ 2 = 42.5° and 85° angle cannot be constructed using compass.

3: False. In a △ the sum of any two sides must be greater than the third side. ∵ AB > BC +AC, such a △ cannot be constructed.

4: True. As AC – AB < BC, i.e., AC < AB + BC.

5: False. Using angle sum property of △ i.e. 180°. As ∠B + ∠C = 105° + 90° = 195° >180°.

6. True. Using angle sum property of △ i.e. 180°. As ∠B + ∠C = 60° + 45° = 105° < 180°.

**Q4 (Fill in the blanks): A triangle can be constructed when its three _______ are given. (sides/angles)**

Answer: sides

**Q5: What type of triangle can be constructed if one side is known.**

Answer: Equilateral triangle.

**Q6(MCQ): With ruler and compass which of the following angles cannot be constructed?**

(a) 60°

(b) 80°

(c) 90°

(d) 105°

Answer: (b) 80°

**Q7(MCQ): With a ruler and compass which of the following angles can be constructed?**

(a) 110°

(b) 100°

(c) 90°

(d) 80°

Answer: (c) 90°

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