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  1. 1. By Rushabh Kaddu Roll no. 23 Std. 9 Div. A
  2. 2. What are Triangles ?? A Triangle is a closed figure which has three sides, three angles and three vertices. On the basis of sides of a triangle, triangles are of three types, an Equilateral Triangle , an Isosceles Triangle and a Scalene Triangle. All triangles are convex and bicentric. That portion of the plane enclosed by the triangle is called the triangle interior, while the remainder is the exterior. NEXT - Types of triangles on the basis of sides of a triangle
  3. 3. EQUILATERAL TRIANGLE - Triangles having all sides equal are called Equilateral Triangle. ISOSCELES TRIANGLE - Triangles having two sides equal are called Isosceles Triangle.
  4. 4. SCALENE TRIANGLE Triangles having no sides equal are called Scalene Triangle.
  5. 5. Congruence of Triangles What is Congruency ? “Congruent” means equal in all respects or figures, whose shapes and sizes, both are the same What are the criteria for Congruence of Triangles ?  SAS Congruence rule  ASA Congruence rule  SSS Congruence rule  RHS Congruence
  6. 6. SAS Congruence Rule If two sides and the angle included between them is equal to the corresponding two sides and the angle between them, of another triangle, then the both triangles are congruent by SAS criteria i.e., Side-Angle-Side Criteria of Congruency
  7. 7. ASA Congruence Rule If two angles and a side of a Triangle are equal to the corresponding two angles and a side of the another Triangle, then the triangles are congruent by the ASA criteria i.e., Angle-Side-Angle Criteria of Congruency.
  8. 8. SSS Congruence Rule If the three sides of one Triangle are equal to the three sides of another Triangle, then the triangles are congruent by the SSS criteria i.e., Side-Side-Side Criteria of Congruency.
  9. 9. RHS Congruence Rule If the hypotenuse, and a leg of one right angled triangle is equal to corresponding hypotenuse and the leg of another right angled triangle then the both triangles are congruent by the RHS criteria i.e., Right Angle-Hypotenuse–Side Criteria of Congruency
  10. 10. Properties And Theorems Angle Sum Property- Angle sum Property of a Triangle is that the sum of all interior angles of a Triangle is equal to 180˚. Exterior Angle Property- Exterior angle Property of a Triangle is that an exterior angle of the Triangle is equal to sum of two opposite interior angles of the Triangle.
  11. 11. Pythagoras Theorem Pythagoras Theorem is a theorem given by Pythagoras. The theorem is that In a Right Angled Triangle the square of the hypotenuse is equal to the sum of squares of the rest of the two sides. HYPOTENUSE
  12. 12. Proof of Pythagoras Theorem
  13. 13. Theorem Theorem 1- Angles opposite to equal side of an isoceles triangle are equal Converse –The sides opposite to equal angles of a triangle are equal Theorem 2- if two sides of a triangle are unequal, the Angle opposite to the longer side is larger (or greater) Theorem 3- in any triangle the side opposite to the larger angle is longer Theorem 4–the sum of any two sides of a triangle is greater than the third side
  14. 14. Formulae for measuring area of triangle Heron’s Formula  Heron’s original formulae which is a universal formulae to find area of any triangle s (s-a) (s-b) (s-c)  Actually it is a generalization on the ideas of Indian scientist “Bharamagupt-650 AD”  David P. Robbins in 1895 presented this formula
  15. 15. Area of triangle Area = ½ (Base x Height) (perpendicular height H) HEIGHT BASE