Properties of a Triangle m  ABC + m  BCA + m  CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m  PAB + m  QBA + m  ACR = 360 0 (Exterior.

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Presentation transcript:

Properties of a Triangle m  ABC + m  BCA + m  CAB = (Internal angles of any triangle add up to ) m  PAB + m  QBA + m  ACR = (Exterior angles of any triangle add up to ) A BC P R Q

Properties of a Triangle (Contd) 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 60 0 each. aa a 60 0 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. Ø0Ø0 Ø0Ø0

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 m  ABC = 90 0 then, l(AC) 2 = l(AB) 2 + l(BC) 2 A BC

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 Units

45°- 45°- 90° Triangle In a 45°- 45°- 90° Triangle, sides opposite to 45 0 angles are of equal length, and, Hypotenuse is sqrt(2) times either side. A B C Units 1 Unit