# Triangle -Types, properties ,similarity and congruency

## Triangle -Types, properties ,similarity and congruency  Triangle -Types, properties ,similarity and congruency What is Triangle?

A two- dimensional shape  closed polygon formed by the three sides and three vertices.
Tri-angel: – tri+angles. Also  we can say triangle is a 3 sided polygon, which has three sides, three vertices and three angles. A triangle with three vertices A,B,C is denoted by   △ABC.

## Properties of triangles:-

Some properties of triangles are listed below.
• A triangle is comprised of 3 sides,3  vertices ,and 3 angles.
• The sum of three interior angles of a triangle is always 180degree.
• The sum of two sides(length) of a triangle is always greater than the length of the third side.
• The area of a triangle is equal to the half of the product of its base and height.
• The side opposite to the greater angle is the longest side of all  the three sides of a triangle.
• The exterior angle of a triangle is always equal to the sum of its interior opposite angles. This property is called as an exterior angle property.
• The sum of all three sides of a triangle is the perimeter of that triangle.
• 1/2*base*height is the formula for area of the triangle.

## Types of triangles:-

Triangle is classified according to its sides and angles.
There are three types of triangle based on sides.
• Equilateral
• Isosceles
• Scalene
Equilateral:-It is a triangle if three sides/line segments equal.
Isosceles:-A triangle having a pair of sides equal is known as isosceles.
Scalene:-A triangle having all three line segments unequal is known as scalene.
There are three types of triangle based on angles.
• Acute
• Obtuse
• Right
Acute:-A triangle is said to be an acute triangle if it’s three angles measuring less than 90 degree.
Obtuse :-A triangle is said to be an obtuse triangle if it is having  one obtuse angle(that is greater than 90degree).A triangle can only have one obtuse angle.
Right :-Right angled triangle is a triangle of having a right angle.
The side opposite to the right angle is hypotenuse.

## Formula’s of triangle:-

Area of triangle is the region occupied by a triangle in two dimensional plane. The dimension of area is square unit. The formula of triangle is given by Area=1/2*base*height.

The perimeter of a triangle is the  length the outer boundary of that triangle. To get the perimeter of a triangle we need to sum the length of the sides .
P=a +b +c .
S=(a +b+ c)/2.  Where S is semi-perimeter and a, b, c are three sides of triangle.
By heron’s formula:-
A=√s(s-a)(s-b)(s-c)

## Similarity and congruency of triangles:-

### Congruent triangles Properties:-

what is congruent– if we place one triangle on another triangle and they cover each other completely, then  we can say triangles are congruent. Some necessary and sufficient conditions for a pair of triangles to be congruent are-
• SAS (side-angle-side):-congruence rule:- two triangles are congruent if two sides and the included angle of one triangle are equal to the sides and the included angle of the other triangle.
• ASA (angle- side-angle):-Two triangles are congruent if two angles and the included side of one triangle are equal to the angles and the included side of other triangle.
• AAS(angle-angle-side):-Two triangles are congruent if two pairs of angle and one pair of corresponding sides are equal.
• SSS(side-side-side):-If three sides of one triangle are equal to the three  sides of another triangle, then the triangles are congruent.
Some more congruent rule:- If in right angled triangle the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other right angled triangle, then the two triangles are congruent.

### Similarity of Triangles:-

Two triangles are similar, if their corresponding angles are equal and their corresponding sides are in the same ratio/proportion.
• If in two triangles corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar. this criterion is known as AAA(angle-angle-angle) criterion of similarity of two triangles.
• If in two triangles, sides of one triangle are proportional to the sides of the other triangle then their corresponding angles are equal and hence the triangles are similar. This criterion is known as the SSS(side-side-side) similarity criterion for two triangles.
• If one angle of a triangle is equal to the one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This criterion is known as the SAS(side-angle-side)similarity criterion for two triangles.

FAQ

### 1. The area of a triangle is 48m2 it base is 8m find the corresponding height.

Ans-Formula for area of Triangle is 1/2*base*height.

Area of Triangle is Given. That is 48m²

.
So 1/2*8*height=48m².

So height=  12m.

### 2. How to take out the area of triangle whose base is 8cm and height is 7cm?

Ans- Formula for area of Triangle is 1/2*base*height.

Here base and height are given.

Only we have to find the area of this triangle.

Area of triangle is=1/2*8*7=28sq cm.

3.

## Triangle- A two dimensional closed shape with three sides and three vertices.

• triangle is comprised of 3 sides, 3 vertices, and 3 angles.
• The sum of three interior angles of a triangle is always 180degree.
• The sum of two sides (length) of a triangle is always greater than the length of the third side.
• The area of a triangle is equal to the half of the product of its base and height.

We know the sum of three interior angles of a triangle is=180°.

•    Here we can consider the smallest angle is x°.
• 3 times of smallest angle=3x°.
• The angle which is 3 times of the smallest angle is half of the greatest angle=3x°.
• Greatest angle is= 6x°.

Now we know the sum of triangle=180°.

We can apply x°+3x°+6x°=180°.

ð 10x°=180°.

= > x°=180°/10=18°.

= > 3x°=3*18=54°.

= > 6x°=6*18°=108°.

If we want to know the angles, then

•         Three angles of this triangles are 18°, 54°, and 108°.
•        According to angles we can tell it is obtuse angle.

4. How many edges are there in a triangle/triangle ki edges kitne hoti hai?

Ans-There are 3 edges/sides of a triangle.

5.  Triangles name in Odisha language?

ANSTriangle is called as Tribhuj in Odisha language.

6.In an isosceles triangle one of its equal angles is 50 degrees then the greatest angle is?

Answer- Isosceles triangle means triangle having a pair of sides equal.

If two sides equal then two angles are also equal in measure.

if one angle is 50 degree of its equal angles then remaining angle

is = 180-(50+50)
= 180-100
=80 degree.
which is also greatest angle.

## FAQS

1.What are 4 types of triangles?
ANS:- There are three types of triangle with respect to its sides.

• Equilateral
• Isosceles
• Scalene
There are three types of triangle with respect to its angles.
• Acute
• Obtuse
• Right
2.What defines a triangle?

ANS:-  A two- dimensional shape  closed polygon formed by the three sides and three vertices.
3.What is a triangle with 2 equal sides?

ANS:- Isosceles:-A triangle having a pair of sides equal is known as isosceles.

4. What are the three properties of a triangle?

ANS:- properties of a triangle are listed below.
• triangle is comprised of 3 sides,3  vertices ,and 3 angles.
• The sum of three interior angles of a triangle is always 180degree.
• The sum of two sides(length) of a triangle is always greater than the length of the third side.
• The area of a triangle is equal to the half of the product of its base and height.
• The side opposite to the greater angle is the longest side of all  the three sides of a triangle.
• The exterior angle of a triangle is always equal to the sum of its interior opposite angles. This property is called as an exterior angle property.