Triangles Class 9 Worksheets

Triangles Class 9 Worksheets

Triangles Class 9 Worksheets play a major role in strengthening the maths concepts.

Triangles Class 9 Worksheet 1 with Answers

1. In the given figure, find the angle marked as x.


2. Find whether the triangle is right-angled, for the sides of the given length.

a. 15, 17, 10               b. 6, 8, 10                   c. 13, 8, 15

3. Two poles 16 m and 10 m high stands upright on a ground. If the distance between their feet is 8 m, then find the distance between their tops.


4. In the given figure, ABC is a triangle in which AB = AC. If BC is produced to D, prove that AD > AC.    

5. The length of the sides of some triangles is given below. Which of them is right-angled? In case of right-angled, name the angle that measures 90°.

a. XY = 12 cm, YZ = 20 cm, ZX = 16 cm

b. DE = 4.1 cm, FD = 0.9 cm, EF = 4.0 cm

6. State true or false.

a. The angles of a triangle are 90°, 30°, 90°.

b. A triangle can have two obtuse angles.

c. In ΔABC, BC > AC implies A > B.

d. The point of concurrency of three medians of a triangle is a centroid.

e. A scalene triangle can be equiangular.

7. What is the correct order of angles of ΔABC from the smallest to the greatest?

8. In the given figure, ABBC and EDFD such that BA = DE and BF = DC. 

Prove that ΔABC  ΔDEF and hence show that AC = EF.


9. The given figure shows the part of roof structure of a school. Show that PQ = PS.

10. In the given figure, ABC is an isosceles triangle with AB = AC and also given that BD = EC. Prove that AE = AD.


11. A tree breaks at a point but did not separate. Its top touches the ground at a distance of 12 m from its base. If it broke at a height of 5 m from the ground, what was the actual height of the tree before it broke?


Triangles Class 9 Worksheet 2 with Answers


1. One of the exterior angles of a triangle is 80° and the interior opposite angles are in the ratio 3 : 5. Find the angles of the triangle.

2. ABC is an isosceles triangle, right-angled at C. Prove that AB2 = 2AC2.

3. ABC is a triangle in which AB = AC. P is any point in the interior of the triangle such that ABP = ACP. Prove that AP bisects BAC.

4. In the given figure, ΔABC is right-angled at C and CD AB. Also A = 65°. Find:

a. ACD

b. CBD

c. BCD


5. In the given figure, prove that

A + B + C + D + E + F = 360°.

6. Compute the value of x in each of the following:

7. Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

8. Fill in the blanks.

a. An exterior angle of a triangle is equal to the sum of the _________.

b. In a triangle, if two sides are equal, then the _________ opposite to those sides are equal.

c. In a triangle, sum of any two sides of a triangle is always _________ the third side.

d. Two rectangles are congruent if they have the same _________.

e. Two circles are congruent if they have the same _________.

9. In the given figure, find ABD. Also, if C = 3 ABC, find ABC.


10. The ratio between the vertical angle and the base angle of an isosceles triangle is 2 : 5. Find the angles of the triangle.

11. AD, BE and CF are the altitudes of ΔABC which are equal. Prove that ΔABC is an equilateral triangle.


Worksheet 1

1. 130°

2. a. No     b. Yes      c. No

3. 10 m

4. Do it yourself

5. a. Right-angled; X

    b. Right-angled; F

6. a. False         b. False

    c. True          d. True

    e. False

7. B < A < C

8. Do it yourself

9. Do it yourself

10. Do it yourself

11. 18 m


Worksheet 2

1. 30°, 50°, 100°

2. Do it yourself

3. Do it yourself

4. a. 25°     b. 25°      c. 65°

5. Do it yourself

6. a. 88°       b. 125°

7. 13 m

8. a. opposite interior angles

    b. angles        c. greater than

    d. dimensions   e. radii

9. 30°; 20°

10. 75°; 75°; 30°

11. Do it yourself

Maths Worksheets for Other Chapters of Class 9

1. Surface area and volume class 9 worksheets

2. Circles class 9 worksheets

3. Area of parallelograms and triangles worksheets

5. Number system class 9 worksheets

6. Polynomials class 9 worksheets

7. Coordinate geometry class 9 worksheets

8. Linear equations in two variables class 9 worksheets

9. Introduction to Euclid’s geometry class 9 worksheets

10. Lines and angles class 9 worksheets

11. Quadrilaterals class 9 worksheet

12. Heron’s formula class 9 worksheet

13. Statistics class 9 worksheets

14. Probability class 9 worksheet


Maths Worksheets for Other Classes

Maths Worksheets for Class 1

Maths Worksheets for Class 2

Maths Worksheets for Class 3

Maths Worksheets for Class 4

Maths Worksheets for Class 5

Maths Worksheets for Class 6

Maths Worksheets for Class 7

Maths Worksheets for Class 8

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