TRIANGLES ITS PROPERTIES AND TYPES
Properties of triangle, types of triangle, median, centroid, incentre orthocentre of triangle, circumcentre
Triangle:
A polygon
with three sides is called a triangle.
Triangle is
a closed figure which have three sides, three angles and three vertices.
Classification of triangles on the bases of sides

These are
of three types:
Scalene Triangle:
A triangle
whose all sides are different is called a scalene triangle.
Isosceles
Triangle:
A triangle
whose two sides are equal is called isosceles triangle.
Equilateral
Triangle:
A triangle
whose all sides are equal is called an equilateral triangle.
Classification of triangles on the basis of angles.

These are
of three types:
Acute
angled triangle:
A triangle whose all angles are acute is called acute angled triangle.
Right
angled Triangle:
A triangle whose one angle equal to 90^{o} is called right.
Obtuse
angled Triangle:
A triangle whose one angle is obtuse is called obtuse angled triangle.
Properties of Triangle
 Sum of all angles of a triangle is equal to 180^{o}.
 Exterior angle of the triangle is equal to the sum of interior opposite angles.
 In triangle angles opposite to the equal sides are equal.
 In triangles angle opposite to the larger side is greater and angle opposite to the smaller side small.
 A triangle is possible if sum of any two sides is greater than the third side.
 Difference of two sides < Third side < Sum of two sides.
 If a line is drawn through the mid points of two sides of triangle then it is parallel to the third side and is half of it.
 If a line is drawn through the mid point of one side of the triangle and is parallel to the second side then it bisect the third side.
Median of
triangle:
A line
segment which join the vertex of the triangle with the midpoint of the
opposite side is called median.
 All medians
of the triangle lie inside the triangle.
 All medians
of equilateral triangles are equal.
 Median divide the triangle into two triangles of equal area.
Centroid of
the triangle :
Point of
concurrence of the medians of the triangle is called its centroid.
The point
inside the triangle where all the medians meet is called Centroid of the triangle.
Centroid of the triangle divide the median in 2 : 1
Altitudes:
A Line
segment from the vertex of the triangle which is perpendicular on the opposite
side is called altitude.
 Altitudes
may be inside or outside of the triangle.
 Altitude of
the acute angled triangle lie inside the triangle.
 Altitude of
right angled triangle lie at the vertex of right angle.
 Altitude of
obtuse angled triangle lie out side the triangle.
 Altitudes
of equilateral triangle are equal.
Orthocenter:
Point of concurrence
of altitudes of the triangle is called orthocenter.
Point at
which all the altitudes meet is called orthocenter.
Circumcenter:
Point of
concurrence of perpendicular bisectors of sides of triangle is called Circumcentre
and the circle which circumscribe the triangle is called circumcircle .
Incentre
:
Point of
concurrence of angle bisectors of the angles of triangle is called Incentre
and the circle inside the triangle and touches all the sides is called
Incircle.
Comments
Post a Comment