9th class Math, Chapter 11: Loci and Construction MCQs

1. A triangle can be constructed if the sum of the measure of any two sides is ____ the measure of the third side.

1. (A) less than
2. (B) greater than ✓
3. (C) equal to
4. (D) greater than and equal to

2. An equilateral triangle ____.

1. (A) can be isosceles ✓
2. (B) can be right angled
3. (C) can be obtuse angled
4. (D) has each angle equal to 50°

3. If the sum of the measures of two angles of a triangle is less than 90°, then the triangle is ____.

1. (A) equilateral
2. (B) acute angled
3. (C) obtuse angled ✓
4. (D) right angled

4. The line segment joining the midpoint of a side to its opposite vertex in a triangle is called ____.

1. (A) median ✓
2. (B) perpendicular bisector
3. (C) angle bisector
4. (D) circle

5. The angle bisectors of a triangle intersect at ____.

1. (A) one point ✓
2. (B) two points
3. (C) three points
4. (D) four points

6. The locus of all points equidistant from a fixed point is ____.

1. (A) circle ✓
2. (B) perpendicular bisector
3. (C) angle bisector
4. (D) parallel lines

7. The locus of points equidistant from two fixed points is ____.

1. (A) circle
2. (B) perpendicular bisector ✓
3. (C) angle bisector
4. (D) parallel lines

8. The locus of points equidistant from a fixed line is/are ____.

1. (A) circle
2. (B) perpendicular bisector
3. (C) angle bisector
4. (D) parallel lines ✓

9. The locus of points equidistant from two intersecting lines is ____.

1. (A) circle
2. (B) perpendicular bisector
3. (C) angle bisector ✓
4. (D) parallel lines

10. The set of all points which are farther than 2 km from a fixed point B is a region outside a circle of radius ____ and centre at B.

1. (A) 1 km
2. (B) 1.9 km
3. (C) 2 km ✓
4. (D) 2.1 km

11. A triangle can be constructed when the lengths of three sides are given only if:

1. (A) all sides are equal
2. (B) one angle is 90°
3. (C) the sum of any two sides is greater than the third ✓
4. (D) the sum of any two sides is less than the third

12. Angles of 30°, 45°, 60°, 90°, 120° can be constructed with:

1. (A) a set square only
2. (B) a ruler only
3. (C) a pair of compasses only ✓
4. (D) a protractor only

13. SSA gives an ambiguous case when the given angle is:

1. (A) obtuse
2. (B) a right angle
3. (C) equal to 180°
4. (D) acute and the opposite side is shorter than the other given side but longer than the height ✓

14. If the angle opposite the given side is obtuse and SSA data are given, the number of possible triangles is:

1. (A) one ✓
2. (B) two
3. (C) none
4. (D) infinite

15. In the ambiguous case, if the side opposite the acute angle equals the height, the number of triangles is:

1. (A) three
2. (B) one ✓
3. (C) two
4. (D) none

16. In the ambiguous case, if the side opposite the acute angle is less than the height, the number of triangles is:

1. (A) one
2. (B) two
3. (C) three
4. (D) none ✓

17. The perpendicular bisector of a line segment:

1. (A) divides it into unequal parts
2. (B) is parallel to it
3. (C) bisects only the angle
4. (D) divides it into two equal parts at right angles ✓

18. A median of a triangle joins a vertex to the:

1. (A) midpoint of an adjacent side
2. (B) opposite vertex
3. (C) midpoint of the opposite side ✓
4. (D) foot of the perpendicular on the opposite side

19. The point of concurrency of the perpendicular bisectors of the sides of a triangle is called the:

1. (A) circumcentre ✓
2. (B) centroid
3. (C) incentre
4. (D) orthocentre

20. The point of concurrency of the medians of a triangle is called the:

1. (A) centroid ✓
2. (B) circumcentre
3. (C) incentre
4. (D) orthocentre