Geometry and Mensuration Worksheet-8

Geometry and Mensuration Worksheet-8

1. If a, b and c are the sides of a Δle, then

(a) a – b > c      (b) c > a + b      (c) c = a + b      (d) b < c + a

2. If the angles of a Δle are in the ratio 1 : 2 : 7 then Δle is

(a) Acute angled                           (b) Obtuse angled

(c) Right angled                            (d) Right angled isosceles

3. A triangle always has

(a) Exactly one acute angle        (b) Exactly two acute angles

(c) At least two acute angles      (d) None of these

4. The number of independent measurements required to construct a Δle is

(a) 3                    (b) 4                    (c) 2                    (d) 5

5. In a ΔABC, if ∠B is an obtuse angle, then the longest side is

(a) AB                 (b) BC                 (c) AC                 (d) None

6. If A : An isosceles Δle is right angled R

R : ∠A = ∠B = 45º and ∠C = 90º

Which of the following statement is true?

(a) A is true and R is correct explanation of A

(b) A is true and R is not the correct explanation of A

(c) A is false

(d) None of these

7. An isosceles Δle can be obtuse angled.

(a) False                                         (b) True

(c) Cannot be determined          (d) None

8. Which of the following statement is correct?

(a) The difference of any two sides is less than the third side

(b) A Δle cannot have two obtuse angles

(c) A Δle cannot have an obtuse angle and a right angle

(d) All of these

9. Two chimneys 18 cm and 13 cm high stand upright in a ground. If their feet are 12 m apart, then the distance between their tops is

(a) 5 cm             (b) 31 m             (c) 13 m              (d) 18 m

10. The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, then the actual height of the tree is

(a) 20 m             (b) 25 m             (c) 30 m             (d) 17 m

11. The point equidistant from the vertices of a triangle is its

(a) Orthocenter                             (b) Centroid

(c) Circum-center                        (d) In-centre

12. The centroid of a triangle is the point of the concurrence of its

(a) Angle bisectors                       (b) Perpendicular bisectors

(c) Altitudes                                   (d) Medians

13. Which of the following statement is true?

(a) The centroid of an acute angled triangle lies in the interior of the triangle.

(b) The orthocenter of an acute angled triangle lies in the interior of the triangle

(c) The circumcentre of an acute angled triangle lies in the interior of the triangle

(d) All of these

14. In ΔABC, D is the midpoint of BC and G is the centroid of the triangle. If GD = 2 cm, then the length of AD is

(a) 4 cm             (b) 6 cm             (c) 2 cm             (d) None of these

15. The incentre of a triangle is equidistant from its

(a) Sides             (b) Vertices       (c) Both              (d) None

16. In a ΔABC, is the midpoint of AC and G is the centroid of the triangle. Then BE : GE

(a) 1 : 2               (b) 2 : 1               (c) 3 : 1               (d) 1 : 3

17. Which of the following statements is true?

(a) The orthocenter of a right angled triangle is the vertex containing right angle

(b) The circumcentre of a right angled triangle is the midpoint of its hypotenuse

(c) The centroid of a right angled triangle lies in the interior of the triangle

(d) All of these

18. In an equilateral triangle, centroid (G), circumcentre (S), orthocentre (H) and incentre (I)

(a) Coincide with each other     (b) Do not coincide with each other

(c) Are collinear points               (d) None of these

19. In general, circumcentre (S), centroid (G) and orthocentrte (H), in any triangle are collinear. G divides H and S in the ratio

(a) 3 : 1               (b) 1 : 2               (c) 2 : 1               (d) 1 : 3

20. Circumcentre (S), centroid (G) and orthocentrte (H), Euler line of a triangle is

(a) Any median                             (b) Any perpendicular bisector

(c) Any altitude                             (d) The line through H, G and S

Answer Key:

(1)-(d); (2)-(b); (3)-(c); (4)-(a); (5)-(c); (6)-(a); (7)-(b); (8)-(d); (9)-(c); (10)-(b); (11)-(c); (12)-(d); (13)-(d); (14)-(b); (15)-(a); (16)-(c); (17)-(d); (18)-(a); (19)-(c); (20)-(d)