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Properties of a Triangle

Properties of a Triangle. P. A. Q. B. C. R. m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 1 80 0 ) mPAB + mQBA + mACR = 360 0 (Exterior angles of any triangle add up to 36 0 0 ). Properties of a Triangle ( Contd ). 60 0. a. a. 60 0. 60 0.

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Properties of a Triangle

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  1. Properties of a Triangle P A Q B C R 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)

  2. Properties of a Triangle (Contd) 600 a a 600 600 Ø0 Ø0 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. 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.

  3. Incenter of a Triangle The point where the three angle bisectors of a triangle meet.

  4. Circumcenter of a Triangle The point where the three perpendicular bisectors of a triangle meet.

  5. Centroid of a Triangle The point where the three medians of the triangle intersect. The 'center of gravity' of the triangle

  6. Orthocenter of a Triangle The point where the three altitudes of a triangle intersect.

  7. Properties of Equilateral Triangle a With an equilateral triangle, the radius of the incircle is exactly half the radius of the circumcircle.

  8. Congruence of Triangles - SSS Test Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.

  9. Congruence of Triangles - SAS Test Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.

  10. Congruence of Triangles - ASA Test Triangles are congruent if any two angles and their included side are equal in both triangles.

  11. 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.

  12. Congruence of Triangles - HL Test Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.

  13. 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

  14. 30°- 60°- 90° Triangle A 600 2 Units 1 Unit 900 300 B C Units 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.

  15. 45°- 45°- 90° Triangle A 450 Units 1 Unit 900 450 C B 1 Unit In a 45°- 45°- 90° Triangle, sides opposite to 450 angles are of equal length, and, Hypotenuse is sqrt(2) times either side.

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