E Board: Suggested Books     ICSE Board:  Foundation Mathematics 
Class 8: Reference Books     Class 8: NTSE Preparation 
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Triangle:  We just studied polygons. Triangle is a polygon with three sides. So, we could define a triangle as a plane closed figure bounded by three line segments.

A triangle is a polygon with three edges and three vertices. It is one of the most basic shapes in geometry. A triangle with vertices A, B, and C is denoted by ∆ABC.

Kind of Triangles

Classification of triangles based on the length of the sides

Scalene Triangle A triangle in which all three sides are of different lengths is called Scalene Triangle.

 

In this type of triangle:

\angle A \neq \angle B \neq \angle C

 t2
Isosceles Triangle A triangle in which two sides are of the same length is called Isosceles Triangle

In this type of triangle:

\angle B = \angle C

 t3
Equilateral Triangle A triangle in which all three sides are of the same length is called Equilateral Triangle.

 

In this type of triangle:

\angle A = \angle B = \angle C

 t4

m14xSome of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

 

Classification of Triangles based on the angles

Acute-angled Triangle A triangle in which all the three angles are more than0^{\circ} and less than 90^{\circ}  is called acute-angled triangle. t5
Right-angles Triangle A triangle in which one of the angles is 90^{\circ} is called right-angled triangle. t6
Obtuse-angled triangle A triangle in which one of the angles is more than 90^{\circ}  but less than 180^{\circ} is called obtuse-angled triangle. t7

m15xSome of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

 

Term related to a Triangle

Median A line segment joining the vertex to the mid-point of the opposite side of a triangle is called median.

In this vertex

A  is meeting at point D (such that BD=DC ) midpoint of BC

t8
Centroid The point of intersection of three medians is called centroid.  

t9

Altitude The perpendicular drawn from the vertex to the opposite side.

Here AD   is the altitude of the triangle AD \ and\  BC is the base.

t10
Orthocenter The intersection of the three altitudes is called the Orthocenter of the triangle.

Here A is the Orthocenter of the triangle.

t11
Angle Bisector A line segment that bisects and interior angle of a triangle is called angle bisector.

Here AD is bisecting \angle BAC into two equal \angle BAD \ and\ \angle DAC

t12
Incentre and Incircle The point of intersection of internal angle bisectors is called the Incentre.

I is the Incentre of the triangle.

Now if you draw a circle with the center

I  in such a way that it touches all the three sides of the triangle, then that is called Incircle.

t13
Perpendicular Bisector or Right Bisector A line bisecting any side of the triangle and perpendicular to it is called perpendicular bisector of that side of the triangle.

Here BC is being bisected by DE. BD=DC \ and\ ED\perp BC.

t14
Circumcenter  and Circumcircle The point of intersection of the perpendicular bisectors of the sides of the triangle is called Circumcenter.

Here O   is the circumcenter.

t15
Exterior Angle and Interior Opposite Angles of a Triangle \angle ACD is the exterior angle and\angle CBA  and\angle BAC   are opposite interior angles of this exterior angle. t16

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

E Board: Suggested Books     ICSE Board:  Foundation Mathematics 
Class 8: Reference Books     Class 8: NTSE Preparation 
--------------------------------------------------------------

 

 

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