This presentation discusses properties of triangles, including: - Classifying triangles by side lengths as scalene, isosceles, or equilateral. - Classifying triangles by angle measures as acute, obtuse, or right. - Defining medians and altitudes of triangles. - Proving properties such as the angle sum theorem, the exterior angle theorem, and Pythagorean theorem.

1. PRESENTATION ON
THETRIANGLE AND
ITS PROPERTIES

2. The Triangle and its Properties
•Triangle
•Triangle
.
.

3. Based on the sides
 Scalene Triangles
 Isosceles Triangles
 Equilateral Triangles
Classification of triangles
Scalene
Isosceles
Equilateral

4. Classification of triangles
Based on Angles
 Acute-angled Triangle
 Obtuse-angled Triangle
°
 Right-angled triangles
Acute
Triangle
Right
Triangle
Obtuse
Triangle

5. MEDIANS OF A TRIANGLE

6. ALTITUDES OF A TRIANGLE
• Altitude – line segment from a vertex
that intersects the opposite side at a
right angle.
Any triangle has three altitudes.

7. ACUTE
OBTUSE
B
A
C
ALTITUDES OF A TRIANGLE

8. Proof: C + D + E = 1800 ……..Straight line
A = D and B = E….Alternate angles
 C + B + A = 1800
A + B + C = 1800
D E
Given: Triangle
A B
C
Construction: Draw line ‘l’ through C parallel
to the base AB
The measure of the three angles of a triangle sum
to 1800 .
To Prove : A + B + C = 1800
l
ANGLE SUM PROPERTY OF A
TRIANGLE

9. An exterior angle of a triangle equals the sum of the
two interior opposite angles in measure.
To Prove: ACD = ABC + BAC
Proof: CB + ACD = 1800 …………………. Straight line
ABC + ACB + BAC = 1800 …………………sum of the triangle
ACB + ACD = ABC + ACB + BAC
ACD = ABC + BAC
A
B C D
Given: In Δ ABC extend BC
to D
EXTERIOR ANGLE OF A TRIANGLE
AND ITS PROPERTY

10. PYTHAGORAS THEOREM
In a right angled triangle the square of the hypotenuse is
equal to the sum of the squares of the other two sides.
In ABC :
• AC is the hypotenuse
• AB and BC are the 2 sides
Then according to Pythagoras theorem ,
A
B C
AC² = AB² + BC²