Ex. 1Multiple choice
With the help of a ruler and a compass, it is possible to construct an angle of :
- (A)35°
- (B)40°
- (C)37.5°
- (D)47.5°
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Solution : Answer (C)
Chapter 11 – Constructions
Class 9 Mathematics · 22 questions · 10 with answers
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Ex. 2Multiple choice
The construction of a triangle ABC in which AB = 4 cm, ∠A = 60° is not possible when difference of BC and AC is equal to:
- (A)3.5 cm
- (B)4.5 cm
- (C)3 cm
- (D)2.5 cm
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Solution : Answer (B) CONSTRUCTIONS 109
Ex. 1Short answerExercise 11.1
An angle of 67.5° can be constructed. 135° 1
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Solution : True. As 67.5° = = (90° + 45°) . 2 2
Ex. 1Short answerExercise 11.2
Construct a triangle ABC in which BC = 7.5 cm, ∠B = 45° and AB – AC = 4 cm.
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Solution : See Mathematics Textbook for Class IX.
Ex. 1Short answerExercise 11.3
Construct an equilateral triangle if its altitude is 6 cm. Give justification for your construction.
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Solution : Draw a line XY. Take any point D on this line. Construct perpendicular PD on XY. Cut a line segment AD from D equal to 6 cm. Make angles equal to 30° at A on both sides of AD, say ∠CAD and ∠BAD where B and C lie on XY. Then ABC is the required triangle. Justification Since ∠A = 30° + 30° = 60° and AD ⊥ BC, ∆ ABC is an equilateral triangle with altitude AD = 6 cm. Fig. 11.1 CONSTRUCTIONS 111
Questions
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°
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(B) 40°
The construction of a triangle ABC, given that BC = 6 cm, ∠ B = 45° is not possible when difference of AB and AC is equal to:
- (A)6.9 cm
- (B)5.2 cm
- (C)5.0 cm
- (D)4.0 cm
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(A) 6.9 cm
The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to :
- (A)3.2 cm
- (B)3.1 cm
- (C)3 cm
- (D)2.8 cm
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(D) 2.8 cm
An angle of 52.5° can be constructed.
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True. As 52.5° = and 210° =180° + 30° which can be constructed.
An angle of 42.5° can be constructed.
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False. As 42.5° = × 85° and 85° cannot be constructed.
A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.
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False. As BC + AC must be greater than AB which is not so.
A triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.
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True. As AC – AB < BC, i.e., AC < AB + BC. ANSWERS 163
A triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.
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False. As ∠B + ∠C = 105° + 90° = 195° >180°.
A triangle ABC can be constructed in which ∠ B = 60°, ∠C = 45° and AB + BC + AC = 12 cm.
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True. As ∠B + ∠C = 60° + 45° = 105° < 180°.
Draw an angle of 110° with the help of a protractor and bisect it. Measure each angle.
Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?
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Yes.
Draw an angle of 80° with the help of a protractor. Then construct angles of
- (i)40°
- (ii)160° and
- (iii)120°.
Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.
Construct a triangle ABC in which BC = 5 cm, ∠B = 60° and AC + AB = 7.5 cm.
Construct a square of side 3 cm.
Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm.
Construct a rhombus whose side is of length 3.4 cm and one of its angles is 45°.
A triangle if its perimeter is 10.4 cm and two angles are 45° and 120°.
A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.
A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm.
An equilateral triangle if its altitude is 3.2 cm.
A rhombus whose diagonals are 4 cm and 6 cm in lengths.