The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.
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This powerpoint includes:
Triangles and Quadrangles
Definition, Types, Properties, Secondary part, Congruency and Area
Definitions of Triangles and Quadrangles
Desarguesian Plane
Mathematician Desargues and His Background
Harmonic Sequence of Points/Lines
Illustrations and Animated Lines.
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Triangles and its properties
1.
2. TRIANGLE
A triangle is a simple closed curved made of
three segments.
A triangle has three sides and three angles ,
and all three sides and angles are called six
elements of the triangle.
A
CB
3. TYPES OF TRIANGLES ON THE
BASIS OF SIDES
Scalene triangle-If all the sides of triangle
are unequal they are called scalene triangle.
Isosceles triangle-If any two sides of a
triangle are
Equal called isosceles triangle.
Equilateral triangle-If all the sides of triangle
are equal it is called equilateral triangle.
4. TYPES OF ANGLES ON THE BASIS OF ANGLES
Acute angled triangle-If all the three angles of a
triangle are acute it is called acute angled
triangle.
Right angled triangle-If one angle of a triangle is
a right angle it is called right angled triangle.
Obtuse angled triangle- if one angle of a triangle
is obtuse it is called obtuse angled triangle.
5. MEDIANS OF A TRIANGLE
The line segment joining a vertex of a
triangle to the midpoint of the opposite side
is called a median of a triangle.
Altitudes of a triangle
The Perpendicular line segment
from a vertex of a triangle to the
opposite side is called an altitude
of the triangle.
6. PROPERTIES OF A TRIANGLE
Exterior angles of a triangle
An exterior angle + adjacent interior
= 180
An exterior angle of a triangle is equal
to sum of its two interior opposite
angles.
7. ANGLE PROPERTY OF A SPECIAL TRIANGLE
Isosceles triangle
A triangle in which length of two
sides are equal called isosceles
triangle.
In a triangle the angles opposite
sides are equal.
In a triangle the sides opposite
equal angles are equal.
8. EQUILATERAL TRIANGLE
A triangle in which all the
three sides are of equal
length is called an
equilateral triangle.
Sum of two sides of triangle
The sum of the length of
any two sides of the triangle
9. PYTHAGORAS PROPERTY
In a right angled triangle the square of
the hypotensure is equal to the sum of
the squares of the other two sides.
In this fig. ab + bc =ac