**Classifying triangles worksheet :**

Classifying triangles worksheet is much useful to the students who would like to practice problems on triangles.

1) Identify the type of triangle whose angles are 35°, 40°, 105°.

2) Identify the type of triangle whose angles are 55°, 65°, 60°.

3) Identify the type of triangle whose angles are 50°, 40°, 90°.

4) Identify the type of triangle whose angles are 45°, 45°, 90°.

5) Identify the type of triangle whose angles are 70°, 70°, 40°.

6) Identify the type of triangle whose angles are 30°, 30°, 120°.

7) Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm.

8) Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm.

9) If (3x + 3) is one of the angles of an acute triangle, then find the value of "x".

10) If 50°, 40° and (2x+4)°are the angles of a right triangle, then find the value of "x".

11) If 2x, y and 3z are the angles of a acute triangle, find the value of "z".

12) If 2x+15, 3x and 6x are the angles of a triangle, identify the type of triangle.

**Problem 1 :**

Identify the type of triangle whose angles are 35°, 40°, 105°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) One of the angles is greater than 90°

From the above two points,

**The given triangle is a scalene and obtuse triangle. **

**Problem 2 :**

Identify the type of triangle whose angles are 55°, 65°, 60°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) All the three angles are less than 90°

From the above two points, we have

**The given triangle is a scalene and acute triangle. **

**Problem 3 :**

Identify the type of triangle whose angles are 50°, 40°, 90°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) One of the angles is 90°

From the above two points, we have

**The given triangle is a scalene and right triangle. **

**Problem 4 :**

Identify the type of triangle whose angles are 45°, 45°, 90°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) One of the angles is 90°

From the above two points, we have

**The given triangle is an isosceles and right triangle. **

**Problem 5 :**

Identify the type of triangle whose angles are 70°, 70°, 40°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) All the three angles are less than 90°

From the above two points, we have

**The given triangle is an isosceles and acute triangle. **

**Problem 6 :**

Identify the type of triangle whose angles are 30°, 30°, 120°.

**Solution :**

Let us consider the following two important points related to the given information.

(i) Two of the given angles are equal

(ii) One of the angles is greater than 90°

From the above two points, we have

**The given triangle is an isosceles and obtuse triangle. **

**Let us look at the next problem on "**Classifying triangles worksheet"

**Problem 7 :**

Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm.

**Solution :**

The length of all the three sides are different.

From the above point, we have

**The given triangle is a scalene triangle.**

**Let us look at the next problem on "**Classifying triangles worksheet"

**Problem 8 :**

Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm.

**Solution :**

The lengths of two of the sides are equal.

From the above point, we have

**The given triangle is an isosceles triangle.**

**Let us look at the next problem on "**Classifying triangles worksheet"

**Problem 9 :**

If (3x + 3) is one of the angles of an acute triangle, then find the value of "x".

**Solution:**

Since the given triangle is acute triangle, all the three angles will be less than 90°.

So, (3x + 3) will also be less than 90°.

Then,

3x + 3 < 90°

3x < 87°

x < 29°

**Hence, the value of "x" is less than 29****°**

**Let us look at the next problem on "**Classifying triangles worksheet"

**Problem 10:**

If 50°, 40° and (2x+4)°are the angles of a right triangle, then find the value of "x".

**Solution:**

Since the given triangle is a right triangle, one of the angles must be 90°

In the given three angles 50°, 40° and (2x+4)°, the first two angles are not right angles.

So the third angle (2x+4)° must be right angle.

Then,

2x + 4 = 90°

2x = 86°

x = 43°

**Hence, the value of "x" is 43****°**

**Let us look at the next problem on "Classifying triangles worksheet"**

**Problem 11 :**

If 2x, y and 3z are the angles of a acute triangle, find the value of "z".

**Solution:**

Since the given triangle is acute triangle, all the three angles will be less than 90°.

So, 3z will also be less than 90°.

Then,

3z < 90°

z < 30°

**Hence, the value of "z" is less than 30****°**

**Let us look at the next problem on "Classifying triangles worksheet"**

**Problem 12 :**

If 2x+15, 3x and 6x are the angles of a triangle, identify the type of triangle.

**Solution:**

Since 2x+15, 3x and 6x are the angles of a triangle, by property

(2x+15) + 3x + 6x = 180°

11x + 15 = 180°

11x = 165°

x = 15°

Plugging x = 15°, we get

First angle = 2x + 15 = 2(15) + 15 = 45°

Second angle = 3x = 3(15) = 45°

Third angle = 6x = 6(15) = 90°

Let us consider the following two important points from the above calculation.

(i) Two of the angles are equal

(ii) One of the angles is 90°

From the above two points, we have

**The given triangle is an isosceles and right triangle. **

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