Properties of a Triangle ABC + mBCA + mCAB = 180 0 Internal angles of any triangle add up to 180 0 ) PAB + mQBA + mACR = 360 0 Exterior angles of any triangle add up to 360 0 ) A B C P R Q
Properties of a Triangle
mABC + mBCA + mCAB = 1800
(Internal angles of any triangle add up to 1800)
mPAB + mQBA + mACR = 3600
(Exterior angles of any triangle add up to 3600)
A
B C
P
RQ
Properties of a Triangle (Contd)
A triangle which has all three of its sides equal in length is calledan equilateral triangle.
All angles of an equilateraltriangle are congruent and measure 600 each.
a a
a
600
600 600
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.
Ø0 Ø0
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
With an equilateral triangle, the radius of the incircle is exactly half the radius of the circumcircle.
a
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
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 mABC = 900 then,l(AC)2 = l(AB)2 + l(BC)2
A
B C
30°- 60°- 90° Triangle
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.
A
B C
2 Units
1 Unit
Units3
600
300900
45°- 45°- 90° Triangle
In a 45°- 45°- 90° Triangle, sides opposite to 450 angles are of equal length, and, Hypotenuse is sqrt(2) times either side.
A
B C
Units1 Unit
1 Unit
2
450
450900