Geometry - Level 1 (Foundation)

https://youtu.be/OXqqyTNefuI

1. Find the sum of interior angles of a hexagon.  (F)

(a) 540°

(b) 600°

(c) 720°

(d) 900°

2. In a triangle, the angles are in the ratio 2:3:4. Find the largest angle.  (F)

(a) 60°

(b) 70°

(c) 80°

(d) 90°

3. Find the length of the hypotenuse of a right triangle with legs 9 cm and 12 cm.  (F)

(a) 13 cm

(b) 14 cm

(c) 15 cm

(d) 16 cm

4. Two triangles are similar with a ratio of corresponding sides 3:5. Find the ratio of their areas.  (F)

(a) 3:5

(b) 6:10

(c) 9:25

(d) 9:15

5. Find the measure of each exterior angle of a regular octagon.  (F)

(a) 36°

(b) 40°

(c) 45°

(d) 50°

6. In a parallelogram, one angle is 70°. Find the measure of an adjacent angle.  (F)

(a) 90°

(b) 100°

(c) 110°

(d) 120°

7. Find the area of an equilateral triangle with side 6 cm.  (F)

(a) 6√3 cm²

(b) 8√3 cm²

(c) 9√3 cm²

(d) 12√3 cm²

8. The diagonals of a rhombus are 16 cm and 12 cm. Find its area.  (F)

(a) 84 cm²

(b) 90 cm²

(c) 96 cm²

(d) 102 cm²

9. Find the radius of a circle whose circumference is 44 cm (use π = 22/7).  (F)

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) 8 cm

10. In a right triangle, one acute angle is 30°. Find the other acute angle.  (F)

(a) 50°

(b) 55°

(c) 60°

(d) 65°

11. Find the length of a chord that is 8 cm from the centre of a circle of radius 17 cm.  (F)

(a) 26 cm

(b) 28 cm

(c) 30 cm

(d) 32 cm

12. The centroid of a triangle divides each median (from vertex to the midpoint of the opposite side) in the ratio  (F)

(a) 1:1

(b) 2:1

(c) 3:1

(d) 3:2

13. Find the number of diagonals in a decagon (10-sided polygon).  (F)

(a) 25

(b) 30

(c) 35

(d) 40

14. If two chords of a circle are equal in length, they are always equidistant from the  (F)

(a) circumference

(b) center

(c) diameter

(d) nearest tangent

15. Find the perimeter of a square whose diagonal is 10√2 cm.  (F)

(a) 30 cm

(b) 35 cm

(c) 40 cm

(d) 45 cm

16. In triangle ABC, AB = AC. If angle B = 50°, find angle A.  (F)

(a) 70°

(b) 75°

(c) 80°

(d) 85°

17. Find the length of the tangent from an external point 13 cm from the centre of a circle of radius 5 cm.  (F)

(a) 10 cm

(b) 11 cm

(c) 12 cm

(d) 13 cm

18. A trapezium has parallel sides of length 10 cm and 14 cm, and height 8 cm. Find its area.  (F)

(a) 80 cm²

(b) 88 cm²

(c) 96 cm²

(d) 100 cm²

19. The sum of the exterior angles of any convex polygon is always  (F)

(a) 180°

(b) 270°

(c) 360°

(d) dependent on the number of sides

20. In a triangle, the orthocentre is the point of intersection of the  (F)

(a) medians

(b) angle bisectors

(c) altitudes

(d) perpendicular bisectors of the sides

21. In triangle ABC, the internal bisector of angle A meets BC at D. If AB = 10, AC = 14, and BC = 18, find BD. 

(a) 6

(b) 7

(c) 7.5

(d) 8

22. Two circles of radii 5 cm and 3 cm touch each other externally. Find the distance between their centres. 

(a) 6 cm

(b) 7 cm

(c) 8 cm

(d) 9 cm

23. In triangle ABC, D and E are the midpoints of AB and AC, respectively. Find the ratio of the area of triangle ADE to the area of triangle ABC. 

(a) 1:2

(b) 1:3

(c) 1:4

(d) 1:5

24. A 25 m ladder is placed against a wall such that it reaches a window 20 m high. Find the distance of the foot of the ladder from the wall. 

(a) 12 m

(b) 13 m

(c) 14 m

(d) 15 m

25. In a circle, two chords AB and CD intersect at a point P inside the circle. If AP = 6, PB = 8, and CP = 4, find PD. 

(a) 8

(b) 10

(c) 12

(d) 14

26. The sides of a triangle are 7 cm, 24 cm, and 25 cm. Find its area. 

(a) 70 cm²

(b) 77 cm²

(c) 84 cm²

(d) 90 cm²

Q27. Rhombus has a perimeter of 12 and one angle = 120°. Find its area

(a)        18√3

(b)        9√3/2

(c)        16√3

(d)        12

Q28. Area of a rhombus with perimeter 48 cm is 96 sq cm. Find the sum of the lengths of its diagonals.

(a)        8√15

(b)        6√3

(c)        3√15

(d)        4√3

29. Two similar triangles have corresponding sides in the ratio 4:7. If the perimeter of the smaller triangle is 24 cm, find the perimeter of the larger triangle. 

(a) 36 cm

(b) 38 cm

(c) 40 cm

(d) 42 cm

30. In triangle ABC, the incircle touches BC, CA, and AB at D, E, and F, respectively. If BD = 3, CD = 4, and the perimeter of the triangle is 24, find AE. 

(a) 4

(b) 4.5

(c) 5

(d) 5.5

Scroll to the bottom for answer key and refer embedded video page for complete Geometry refresher and also solutions to these 20 foundation questions or visit @iimwalabanda YouTube page

Also, few properties I missed in the concept video are

1. Angle bisector theorem. It says that Bisector of any angle will divide the opposite side in the ratio of the sides containing the angle

2. Geometric mean theorem. It says that in a right angled triangle, if an altitude is drawn from the right angle to the hypotenuse, the length of that altitude is the geometric mean of the lengths of the two segments it creates on the hypotenuse

3. Appollonius Theorem derivation (No need to learn the theorem, once we cover cosine law in Trignometry , you can deal with it easily. Still look at the derivation if curious!)

4. Triangle Inequality Theorem Sum of two sides in a triangle is greater than third side and difference of two sides is less than the third side. (Please note, I mentioned equality case to be true in video which is incorrect)

5. It is worth noting that by relation between squares of sides, one can determine nature of triangle (Acute, Right angled or Obtuse)

Q.No	Correct Option	Q.No	Correct Option
Q1	C (720°)	Q16	C (80°)
Q2	C (80°)	Q17	C (12 cm)
Q3	C (15 cm)	Q18	C (96 cm²)
Q4	C (9:25)	Q19	C (360°)
Q5	C (45°)	Q20	C (altitudes)
Q6	C (110°)	Q21	C (7.5)
Q7	C (9√3 cm²)	Q22	C (8 cm)
Q8	C (96 cm²)	Q23	C (1:4)
Q9	C (7 cm)	Q24	D (15 m)
Q10	C (60°)	Q25	C (12)
Q11	C (30 cm)	Q26	C (84 cm²)
Q12	B (2:1)	Q27	B (9√3/2)
Q13	C (35)	Q28	A(8√15)
Q14	B (centre)	Q29	D (42 cm)
Q15	C (40 cm)	Q30	C (5)