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
Draw any X triangle XYZ and name its sides, angles and vertices.
Sides are XY, YZ and ZX
Angles are ∠XYZ, ∠YZX and ∠YXZ
Vertices are X, Y and Z
How many triangles are there in each of the following figures?
(a) 3 triangles
(b) 5 triangles
(c) 8 triangles
(d) 8 triangles
Identify the following triangles on the basis of their angles.
(a) Right angled triangle
(b) Obtuse angled triangle
(c) Acute angled triangle
(d) Acute angled triangle
Can you construct a triangle with angles of measure 70°, 40°, 60°? Why or why not?
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°.
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
(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.
One of the angles of a right angled triangle is 40°.
Find the other angles of the triangle.
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°.
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?
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° > 90°
Hence the triangle is obtuse angled triangle.
Write ‘True’ or ‘False’ for the following statements:
(a) The sum of three angles of a triangle is always equal to 180°.
(b) A triangle can have two of its angles greater than 90°.
(c) Equilateral triangle has all of its three sides equal in length.
(d) One angle of a right angled triangle is always equal to 90°.
(e) A triangle whose all the three sides are different in length is called an isosceles triangle.
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.