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