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Properties of a Triangle
P
A
Q
B
C
mABC + mBCA + mCAB = 1800
(Internal angles of any triangle add up to 1800)
mPAB + mQBA + mACR = 3600
(Exterior angles of any triangle add up to 3600)
R
Properties of a Triangle (Contd)
600
a
a
600
600
a
A triangle which has
all three of its sides
equal in length is called
an equilateral triangle.
All angles of an equilateral
triangle are congruent and
measure 600 each.
Ø0
Ø0
A triangle which has
two of its sides equal in length
is called an isosceles triangle.
The base angles of an isosceles
triangle are always equal.
Incenter of a Triangle
The point where the three angle bisectors of a triangle meet.
Circumcenter of a Triangle
The point where the three perpendicular bisectors of a triangle meet.
Centroid of a Triangle
The point where the three medians of the triangle intersect.
The 'center of gravity' of the triangle
Orthocenter of a Triangle
The point where the three altitudes of a triangle intersect.
Properties of Equilateral Triangle
a
With an equilateral triangle, the radius of the incircle is exactly half
the radius of the circumcircle.
Congruence of Triangles - SSS Test
Triangles are congruent if all three sides in one triangle are
congruent to the corresponding sides in the other.
Congruence of Triangles - SAS Test
Triangles are congruent if any pair of corresponding sides and their
included angles are equal in both triangles.
Congruence of Triangles - ASA Test
Triangles are congruent if any two angles and their included side are
equal in both triangles.
Congruence of Triangles - AAS Test
Triangles are congruent if two pairs of corresponding angles and a
pair of opposite sides are equal in both triangles.
Congruence of Triangles - HL Test
Two right triangles are congruent if the hypotenuse and one
corresponding leg are equal in both triangles.
Pythagoras Theorem
A
B
C
In a right triangle, the square of the hypotenuse is equal to the
sum of the squares of the other two sides.
In  ABC if mABC = 900 then,
l(AC)2 = l(AB)2 + l(BC)2
30°- 60°- 90° Triangle
A
600
2 Units
1 Unit
900
B
300
3 Units
C
In a 30°- 60°- 90° Triangle, the hypotenuse is double the side opposite to 30° angle
and the side opposite to 60° angle is Sqrt(3) times the side opposite to 30° angle.
45°- 45°- 90° Triangle
A
450
2
1 Unit
900
B
Units
450
1 Unit
C
In a 45°- 45°- 90° Triangle, sides opposite to 450 angles are of equal length, and,
Hypotenuse is sqrt(2) times either side.