Class 9 Maths Chapter Triangles

1. FUN WITH
TRIANGLES
WELCOME TO THE WORLD OF TRIANGLES

2. INTRODUCTION
C
A
WeKnow That A Closed
Figure Formed By Three
Intersecting Lines Is Called
A Triangle(‘tri’ Means
‘Three’). A Triangle Has
Three Sides, Three Angles
And Three Vertices.
For Example –
In Triangle ABC, Denoted As
∆ABC, AB, BC And CA Are The
Three Sides, ∠A, ∠B ,∠C Are
Three Angles And A, B, C Are
Three Vertices.
B

3. Congruence of Triangles
A
B
C
P
Q
R
Two Triangles Are Congruent
If The Sides And Angles Of
One Triangle Are Equal To The
Corresponding Sides And
Angles Of The Other Triangle.
If ∆PQR Is Congruent To ∆ABC,
We Write ∆PQR = ∆ABC.
Congruent Triangles
Corresponding Parts Are
Equal And We Write In Short
‘CPCT’ For Corresponding
Parts Of Congruent
Triangles.

4. SAS 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.

5. ASA congruence rule
Two Triangles
Are Congruent
If Two Angles
And The
Included Side
Of One Triangle
Are Equal To
The Angles And
The Included
Side Of The
Other Triangle.

6. AAS congruence rule
Two Triangles
Are Congruent If
Two Angles And
The Non-Included
Side Of One
Triangle Are
Equal To The
Angles And The
Non-Included
Side Of The
Other Triangle.

7. SSS congruence rule
Two Triangles
Are Congruent
If Three Sides
Of One
Triangle Are
Equal To The
Sides Of The
Other
Triangle.

8. RHS congruence rule
Two Triangles
Are Congruent
If In Two Right
Triangles,
Hypotenuse
And One Side Of
A Triangle Are
Equal To The
Hypotenuse
And One Side Of
Other Triangle

9. Inequalities in a Triangle
(i) If two sides of a triangle are
unequal, the angle opposite to
the longer side is larger (or
greater).
(ii) In any triangle, the side
opposite to the larger (or
greater) angle is longer.
(iii) The sum of any two sides of
a triangle is greater than the
third side, i.e., AB + BC > CA.

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PREPARED BY – VYOM BHARDWAJ
Class – 9th B
Roll number - 37