The DAV Maths Book Class 6 Solutions and **DAV Class 6 Maths Chapter 12 Worksheet 1 **Solutions of Triangles offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 12 WS 1 Solutions

Question 1.

Draw any X triangle XYZ and name its sides, angles and vertices.

Answer:

In ΔXYZ,

Sides are XY, YZ and ZX

Angles are ∠XYZ, ∠YZX and ∠YXZ

Vertices are X, Y and Z

Question 2.

How many triangles are there in each of the following figures?

Answer:

(a) 3 triangles

(b) 5 triangles

(c) 8 triangles

(d) 8 triangles

Question 3.

Identify the following triangles on the basis of their angles.

Answer:

(a) Right angled triangle

(b) Obtuse angled triangle

(c) Acute angled triangle

(d) Acute angled triangle

Question 4.

Can you construct a triangle with angles of measure 70°, 40°, 60°? Why or why not?

Answer:

Sum of the angles

= 70° + 40° + 60° = 170°

No, we cannot construct this triangle as the sum of all the angles of a triangle is not 180°.

Question 5.

Can you construct a triangle using line segments of the following lengths?

(a) 7 cm, 3 cm, 12 cm

(b) 6 cm, 5 cm, 11 cm

Answer:

(a) As per the property of triangle, the lengths of any two sides of a triangle must be greater than the length of the third side.

Here 3 cm + 7 cm = 10 cm

10 cm < 12 cm

Hence, it is not possible to construct this triangle.

(b) Here 5 cm + 6 cm =11 cm

11 cm =11 cm

The sum of two sides is equal to the third side of the triangle.

Hence, the triangle is not possible to be constructed.

Question 6.

One of the angles of a right angled triangle is 40°.

Find the other angles of the triangle.

Answer:

Let us take a right angled triangle ABC, in which ZB = 90°

∠A + ∠C = 90°

[Remaining angles of the triangle]

40° + ∠C = 90°

∠C = 90° – 40° = 50°

Hence the third angle is 50°.

Question 7.

Two angles of a triangle measure 30° and 55° respectively. Find the measures of the third angle. Also state what type of triangle is it?

Answer:

Sum of the three angles of a triangle = 180°

Measure of two angles = 30° and 55°

∴ Measure of the third angle

= 180°-(30°+ 55°)

= 180° – 85°

= 95°

95° > 90°

Hence the triangle is obtuse angled triangle.

Question 8.

Write ‘True’ or ‘False’ for the following statements:

(a) The sum of three angles of a triangle is always equal to 180°.

Answer:

True

(b) A triangle can have two of its angles greater than 90°.

Answer:

False

(c) Equilateral triangle has all of its three sides equal in length.

Answer:

True

(d) One angle of a right angled triangle is always equal to 90°.

Answer:

True

(e) A triangle whose all the three sides are different in length is called an isosceles triangle.

Answer:

False

### DAV Class 6 Maths Chapter 12 Worksheet 1 Notes

A figure enclosed by three line segments is called a triangle. It has 3 angles and 3 sides.

Types of Triangle

1. Scalene triangle:

The triangle having all the sides of different lengths is called scalene triangle. In the given figure, AB ≠ BC ≠ AC.

2. Isosceles triangle:

The triangle whose any two sides are equal is called isosceles triangle.

In the given figure, AB = AC.

3. Equilateral triangle:

The triangle whose all sides are equal is called equilateral triangle. In the given figure, AB = BC = CA

4. Acute angled triangle: The triangle in which each angle is acute is called acute angled triangle.

Here, in ΔPQR, all angles are acute.

5. Right angled triangle: The triangle whose one angle is 90° is called right angled triangle.

Here, in ΔPQR, ∠Q = 90°.

6. Obtuse angled triangle: The triangle in which only one angle is obtuse is called obtuse angled triangle.

Here, ∠B is obtuse angle.