This PPT was done by me for IX Grade Seminar TRIANGLES

1. By
Rushabh Kaddu
Roll no. 23
Std. 9 Div. A

2. What are Triangles ??
A Triangle is a closed figure which has three sides, three angles and
three vertices. On the basis of sides of a triangle, triangles are of three types,
an Equilateral Triangle , an Isosceles Triangle and a Scalene Triangle.
All triangles are convex and bicentric. That portion of the plane enclosed by
the triangle is called the triangle interior, while the remainder is the exterior.
NEXT - Types of triangles on the basis of sides of a triangle

3. EQUILATERAL TRIANGLE -
Triangles having all sides equal are called Equilateral Triangle.
ISOSCELES TRIANGLE -
Triangles having two sides equal are called Isosceles Triangle.

4. SCALENE TRIANGLE
Triangles having no sides equal are called Scalene Triangle.

5. Congruence of Triangles
What is Congruency ?
“Congruent” means equal in all respects or figures, whose shapes and
sizes, both are the same
What are the criteria for Congruence of Triangles ?
 SAS Congruence rule
 ASA Congruence rule
 SSS Congruence rule
 RHS Congruence

6. SAS Congruence Rule
If two sides and the angle included between them is
equal to the corresponding two sides and the angle
between them, of another triangle, then the both
triangles are congruent by SAS criteria i.e.,
Side-Angle-Side Criteria of Congruency

7. ASA Congruence Rule
If two angles and a side of a Triangle are equal to the
corresponding two angles and a side of the another
Triangle, then the triangles are congruent by the ASA
criteria i.e.,
Angle-Side-Angle Criteria of Congruency.

8. SSS Congruence Rule
If the three sides of one Triangle are equal to the three
sides of another Triangle, then the triangles are
congruent by the SSS criteria i.e.,
Side-Side-Side Criteria of Congruency.

9. RHS Congruence Rule
If the hypotenuse, and a leg of one right angled
triangle is equal to corresponding hypotenuse and the leg
of another right angled triangle then the both triangles
are congruent by the RHS criteria i.e.,
Right Angle-Hypotenuse–Side Criteria of Congruency

10. Properties And Theorems
Angle Sum Property-
Angle sum Property of a Triangle is that the sum of all
interior angles of a Triangle is equal to 180˚.
Exterior Angle Property-
Exterior angle Property of a Triangle is that an exterior
angle of the Triangle is equal to sum of two opposite interior
angles of the Triangle.

11. Pythagoras Theorem
Pythagoras Theorem is a theorem given by Pythagoras.
The theorem is that In a Right Angled Triangle the square of the
hypotenuse is equal to the sum of squares of the rest of the two sides.
HYPOTENUSE

12. Proof of Pythagoras Theorem

13. Theorem
Theorem 1- Angles opposite to equal side of an isoceles
triangle are equal
Converse –The sides opposite to equal angles of a
triangle are equal
Theorem 2- if two sides of a triangle are unequal, the
Angle opposite to the longer side is larger (or greater)
Theorem 3- in any triangle the side opposite to the larger
angle is longer
Theorem 4–the sum of any two sides of a triangle is
greater than the third side

14. Formulae for measuring area of triangle
Heron’s Formula
 Heron’s original formulae which is a universal
formulae to find area of any triangle
s (s-a) (s-b) (s-c)
 Actually it is a generalization on the ideas of Indian
scientist “Bharamagupt-650 AD”
 David P. Robbins in 1895 presented this formula

15. Area of triangle
Area = ½ (Base x
Height) (perpendicular height
H)
HEIGHT
BASE