**Triangles
Class 9 Worksheets**

**Triangles Class 9 Worksheets** play a vital role in strengthening the maths
concepts. After studying the concepts of mathematics, revision of **Triangles Class 9 Worksheets** is very important for the students. This
assesses the preparation of the students. Students can assess themselves by its
own by solving the **Triangles Class 9 Worksheets**. Parents and teachers can also assess
the students by giving them these **Triangles Class 9 Worksheets** to solve.

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by the teachers using these **Triangles Class 9 Worksheets**.

**Triangles
Class 9 Worksheet 1**

**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 Î”ABC, 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 Î”ABC
from the smallest to the greatest?

**8. **In the given figure, AB⊥BC and ED⊥FD such that BA = DE and BF = DC.

Prove that Î”ABC ≅ Î”DEF
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**

**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 AB^{2} = 2AC^{2}.

**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, Î”ABC 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 Î”ABC which are equal. Prove that Î”ABC is an
equilateral triangle.

**ANSWERS**

**Worksheet 1**

1. 130°

2. a. No b. Yes
c. No

3. 10 m

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

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** **

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