this presentation is based on the types and properties of triangles

1. PROPERTIES OF TRIANGLE
presented by,
JYOTI S SORATUR
Roll no:60
kle’s college of education, hubli

2. CONTENTS
1.Theorem- Angles opposite to equal sides of an isoceles
triangles are equal.
2. Inequalities of a triangle
Statement- In any triangle the side of opposite to the
greater angle is longer.

4. J:Triangles _ Educational Video for
Kids - YouTube (360p).mp4

5. 1. ANGLES OPPOSITE TO EQUAL SIDES OF AN ISOCELES
TRIANGLE ARE EQUAL.
ABC is a isosceles triangle
In which AB=AC
To prove- 𝐵 = 𝐶
Let us draw a bisector of 𝐴 and
let D be the point of
intersection of this bisector
of 𝐴 = 𝐵𝐶
From ∆BAD and ∆CAD
AB=AC
𝐵𝐴𝐷 = 𝐶𝐴𝐷

6. AD=AD
∴ ∆𝐵𝐴𝐷 ≅ ∆𝐶𝐴𝐷
SAS rule- Two triangles are congruent if
two sides and the sssincluded angle of
an triangle are equal to the two sides and
the included angle of the other.
So, 𝐴𝐵𝐷 = 𝐴𝐶𝐷
since they are corresponding angles of
congruent triangles.
So, 𝐵 = 𝐶
B C
A
D

7. INEQUALITIES IN A TRIANGLE
Theorem- In any triangle the side
opposite to the larger angle is
longer.
To prove- we have to consider a
scalene triangle
Let me consider a ∆ABC whose
sides are AB=2 cm BC=3 cm
CA=4 cm
We have to find AB+BC BC+AC
AC+AB
A triangle in which all sides are of
different lengths.

8. After finding this we will observe that,
AB + BC > 𝐴𝐶
BC + AC > 𝐴𝐵
𝐴𝐶 + 𝐴𝐵 > 𝐵𝐶
∴ 𝐴𝐵 + 𝐵𝐶 = 2 + 3 = 5 𝑐𝑚 > 4 𝑐𝑚 = 𝐴𝐶
𝐵𝐶 + 𝐴𝐶 = 3 + 4 = 7 𝑐𝑚 > 2 𝑐𝑚 = 𝐴𝐵
𝐴𝐶 + 𝐴𝐵 = 4 + 2 = 6 𝑐𝑚 > 3 𝑐𝑚 = 𝐵𝐶
Hence the proof 3 cm CB
A

9. J:Triangle Inequality Theorem - Example -
YouTube (360p).mp4
J:Side opposite to greater angle is longer in
a triangle (Theorem and Proof) - YouTube
(360p).mp4

10. 1.In ∆𝐴𝐵𝐶 the bisector AB of 𝐴 is perpendicular to side BC.
Showthat AB=AC and ∆𝐴𝐵𝐶 is isosceles.
In ∆𝐴𝐵𝐷 and ∆𝐴𝐶𝐷
𝐵𝐴𝐷 = 𝐶𝐴𝐷
𝐴𝐷 = 𝐴𝐷
𝐴𝐷𝐵 = 𝐴𝐷𝐶 = 90°
SO, ∆𝐴𝐵𝐷 ≅ ∆𝐴𝐶𝐷
∴ 𝐴𝐵 = 𝐴𝐶
∆𝐴𝐵𝐶 is an isosceles triangle
A
D CB