Triangles and their Properties Maths - Triangles and their Properties

As seen above, ∆ABC has three sides. Line segment AB is one side. Write the names of the other two sides. ∆ABC has three angles. ∠ABC is one among them. Write the names of the other angles.

In the given figure, some points and some line segments joining them have been drawn. Which of these figures is a triangle? Which figure is not a triangle? Why not?

The lengths of the three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
i. 17 cm, 7 cm, 8 cm
ii. 7 cm, 24 cm, 25 cm
iii. 9 cm, 6 cm, 16 cm
iv. 8.4 cm, 16.4 cm, 4.9 cm
v. 15 cm, 20 cm, 25 cm
vi. 12 cm, 12 cm, 16 cm

The lengths of the sides of some triangles are given. Say what types of triangles they are.

1. 3 cm, 4 cm, 5 cm
2. 3.4 cm, 3.4 cm, 5 cm
3. 4.3 cm, 4.3 cm, 4.3 cm
4. 3.7 cm, 3.4 cm, 4 cm

As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.

Observe the figures below and write the type of the triangle based on its sides:

Observe the figures below and write the type of the triangle based on its angles:

Draw any triangle on a paper. Name its vertices A, B, C. Measure the lengths of its three sides using a divider and scale and enter them in the table.

Length of side	Sum of the lengths of two sides	Length of the third side
l (AB) = cm	l (AB) + l (BC) = cm	l (AC) = cm
l (BC) = cm	l (BC) + l (AC) = cm	l (AB) = cm
l (AC) = cm	l (AC) + l (AB) = cm	l (BC) = cm

Properties of a triangle
Take a triangular piece of paper and make three different types of marks near the three angles. Take a point approximately at the center of the triangle. From this point, draw three lines that meet the three sides. Cut the paper along those lines. Place the three angles side by side as shown. See how the three angles of a triangle together form a straight angle, or, an angle that measures 180°.

Properties of a triangle.
Take a triangular piece of paper. Choose three different colors or signs to mark the three comers of the triangle on both sides of the paper. Fold the paper at the midpoints of two sides as observe?

Observe the set squares in your compass box. What kind of triangles are they?

Measure all the angles of the triangles given below. Enter them in the following table.

In ∆DEF	In ∆PQR	In ∆LMN
Measure of ∠D = m ∠D =___	Measure of ∠P = m ∠P =___	Measure of ∠L =__
Measure of ∠E = m ∠E =___	Measure of ∠Q =___=___	Measure of ∠M =___
Measure of ∠F = ___=___	Measure of ∠R =___=___	Measure of ∠N =___
Observation:All three angles are acute angles.	Observation:One angle is right angle and two are acute angles.	Observation:One angle is an obtuse angle and two are acute.