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Geometric Constructions CBSE Class 9

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Question 1/20

Q 1. If PQR is an equilateral triangle, then which of the following is true? 

Solution

All the sides of an equilateral triangle are equal.

Q 2. In an equilateral triangle, the angle bisector divides the angle into two equal angles of 

Solution

Angles of an equilateral triangle are 60° each, so each half is 30°.

Q 3. Any point on the angle bisector 

Solution

Any point on the angle bisector is equidistant from the arms of the angle.

Q 4. Which of the triangles can be constructed by just measuring the altitude? 

Solution

An equilateral triangle can be constructed by just measuring the altitude.

Q 5. If ABT = CBT, then which of the following statements is possible? 

Solution

Out of the given statements, 'BT is the angle bisector of ABC.’ is the only one possible.

Q 6. If OC is the perpendicular bisector of AB such that C lies on AB = 10 cm, then 

Solution

If OC is the perpendicular bisector of AB such that C lies on AB, then AC = BC = ½ AB.

Q 7. To construct a scalene triangle, we need 

Solution

To construct a scalene triangle, we need two sides and the included angle.

Q 8. Using a compass, we can construct a 100° angle using the property of the 

Solution

Using a compass, we can construct a 100° angle using the property of the equilateral triangle.

Q 9. If 80° is bisected twice, then what will be the measure of each part? 

Solution

If 80° is bisected twice, then the measure of each part will be 20°. 

Q 10. Which triangle can be constructed by knowing just one of its sides? 

Solution

An equilateral triangle can be constructed by knowing just one of its sides.

Q 11. ST is the perpendicular bisector of UV such that S lies on UV. If ST = 3 cm and UV = 8 cm, then TU = 

Solution

US = ½ UV = 4 cm  (ST is the perpendicular bisector of UV)

So, UST is a right-angled triangle.

UT2 = US2 + ST2

Q 12. If 30° is bisected, then what will be the measure of each part? 

Solution

If 30° is bisected, then the measure of each part will be 15°. 

Q 13. In ABC, A = 30° and C = 60° cm, then which of the following is required to complete the triangle? 

Solution

We need the measurement of one of the sides to complete the triangle.

Q 14. PQ is the bisector of TPS. If m QPT = 52°, then m SPT = 

Solution

PQ is the bisector of TPS. If m QPT = 52°, then m SPT = 2m QPT = 104°.

Q 15. An angle can have 

Solution

An angle can have only one bisector. 

Q 16. Which of the following is true? 

Solution

In an isosceles triangle, both base angles are equal.

Q 17. In DXYZ, X = 30°, Y = 50°, then to complete the construction, we need 

Solution

To construct XYZ such that X = 30°, Y = 50°, we need the length of XY. Or we can find Z and use XZ or YZ to complete the triangle

Q 18. If point X is equidistant from the arms of ABC, then which of the following is true? 

Solution

If point X is equidistant from the arms of ABC, then it will lie on the angle bisector of ABC.

Q 19. AB is the perpendicular bisector of UV such that B lies on UV. If AU = 13 cm and AB = 12 cm, then UV = 

Solution

So, ABU is a right-angled triangle.

UA2 = AB2 + UB2

2UB = UV = 10 cm

Q 20. In ABC, B = C = 45°, then which of the following is true? 

Solution

A = 90° 

So,

ABC is a right-angled isosceles triangle.

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Asked by anuragsharma03jp 16th March 2019, 12:05 AM
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