Learning Objectives
● To apply angle sum property of triangles.
● To understand the concept of congruency of triangles.
● To know the criteria for congruence of triangles.

__Chapter 4__

__GEOMETRY__

** **

**Learning Objectives**

● To apply angle sum property of triangles.

● To understand the concept of congruency
of triangles.

● To know the criteria for congruence
of triangles.

** **

__Recap__

**Triangles**

In first term we studied about different types of angles made by intersecting lines and parallel lines with transversals. Further we learnt about triangles, types of triangles and properties of triangles. In this term we are going to apply the properties of triangles.

A triangle is a closed
figure formed by three line segments. It has three vertices, three sides and three
angles.

In the triangle *ABC* (Fig 4.1)
vertices are *A,B,C,* the sides are and the
angles are ∠CAB , ∠ABC , ∠BCA . We have already learnt to classify
triangles based on sides and angles.

The classification of triangles are shown
below.

In any triangle drawn by joining three
non-collinear points, the sum of the lengths of any two sides is greater than the
length of the third side. This property is called as Triangle
inequality.

To verify this property, let us consider
three types of triangles based on angles.

For each of these triangles the following
statements are true.

1.* a + b > c *

2.* b + c > a *

3.* c + a > b *

This property is also true for three
types of triangles based on sides.

** **

**Try these**

**Anwser the following questions.**

1. Triangle is formed by
joining three ** non–collinear** points.

2. A triangle has ** three** vertices and

3. A point where two sides
of a triangle meet is known as ** Vertex** of a triangle.

4. Each angle of an equilateral
triangle is of ** 60°** measure.

5. A triangle has angle
measurements of 29°, 65° and 86°. Then it is _______ triangle.

(i) an acute angled (ii)
a right angled (iii) an obtuse angled (iv) a scalene

** Answer:** (i) an acute angled.

6. A triangle has angle
measurements of 30°, 30° and 120°. Then it is _______ triangle.

(i) an acute angled (ii)
scalene (iii) obtuse angled (iv)
right angled

** Answer :** (iii) obtuse angled

**7. Which of the following
can be the sides of a triangle?**

(i) 5,9,14 (ii) 7,7,15 (iii) 1, 2, 4 (iv) 3, 6, 8

**(i) 5,9,14 5+9 =
14, 14 = 14 can be side of the triangle**

**(ii) 7, 7,15 7+7 =
14 < 15 can’t be side of the triangle**

**(iii) 1,2,4 1+ 2 =
3< 4 can’t be side of the triangle can be side of the triangle**

**(iv) 3, 6,8 3 + 6 =
9 > 8 can be side of the triangle**

*Answer :*

(iv) 3, 6,8

3 + 6 = 9 > 8 can be side of the triangle

**8. ****Ezhil wants to fence his
triangular garden. If two of the sides measure 8 feet and 14 feet then the length
of the third side is __________**

(i) 11 ft (ii) 6 ft (iii) 5 ft (iv) 22 ft

** Answer :** (iv) 22ft

**9. ****Can we have more than one
right angle in a triangle?**

No, it cannot.

**10. How many obtuse angles
are possible in a triangle?**

One.

**11. In a right triangle,
what will be the sum of other two angles?**

90°

**12. Is it possible to form an isosceles right angled triangle? Explain.**

Yes. It is possible.

Side AB = Side BC=3cm

∠B = 90°

** **

__Introduction__

Triangles are an effective tool for construction
and architecture. They are used in the design of buildings and other structures
for more strength and stablility. The knowledge of the properties of triangles is
essential to understand its use in architecture. The triangle’s use in architecture
dates back more years than other common shapes like dome, arch, cylinder. Usage
of triangles even predates the wheel. The most sturdy of the triangles are equilateral
and isosceles; their symmetry aids in distributing weight.

This chapter is a continuation of properties
of triangles that we studied in class VI.

** **

**MATHEMATICS ALIVE - Geometry
in Real Life**

Tags : Term 2 Chapter 4 | 7th Maths , 7th Maths : Term 2 Unit 4 : Geometry

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