Triangles
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Transcript

  • 1. Triangles1.
  • 2. What are triangles ?? ??1.
  • 3. Types of Triangles 2
  • 4. On Basis of Length of Sides, there are 3 types of Triangles • Equilateral Triangle • Isosceles Triangle • Scalene Triangle On Basis of Angles, there are 3 types of triangles • Acute Angled Triangle • Obtuse Angled Triangle • Right Angled Triangle TYPES OF TRIANGLES
  • 5. Properties A Triangle. 3
  • 6. Properties Pythagorus theoram Exterior angle property Angle sum property
  • 7. • 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 • Pythagorus theoram- 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.
  • 8. Properties of an isosceles triangle • Angle opposite to the equal sides of an isosceles triangle are equal. • The sides opposite to the equal angles of a triangle are equal.
  • 9. Secondary Parts Triangle. 4
  • 10. 1. The Line Segment joining the midpoint of the base of the Triangle is called Median of the Triangle. OR 2. A Line Segment which connects a vertex of a Triangle to the midpoint of the opposite side is called Median of the Triangle. MEDIAN
  • 11. Altitudes of a triangle The Line Segment drawn from a Vertex of a Triangle perpendicular to its opposite side is called an Altitude or Height of a Triangle. ALTITUDE
  • 12. Perpendicular bisector A line that passes through midpoint of the triangle or the line which bisects the third side of the triangle and is perpendicular to it is called the Perpendicular Bisector of that Triangle. Perpendicular Bisector
  • 13. Angle Bisector A line segment that bisects an angle of a triangle Is called Angle Bisector of the triangle. ANGLE BISECTOR
  • 14. Congruency OF A Triangles 5
  • 15. •Two figures are congruent, if they are of the same shape and of the same size. •Two circles of the same radii are congruent. •Two squares of the same sides are congruent.
  • 16. SSS criteria of congruency 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. SSS criteria is called Side- Side-Side criteria of congruency.
  • 17. SAS criteria of congruency 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.
  • 18. ASA criteria of congruency If two angles and a side of a Triangle is 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.
  • 19. AAS criteria of congruency If two angles and one side of one triangle are equal to angles to two angles and the corresponding side of the other triangle then the two triangles are congruent
  • 20. RHS criteria of congruency 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.
  • 21. Inequalities A Triangle. 6
  • 22. • In a triangle ,angle opposite to the longer side is larger. • In a triangle, side opposite to the larger(greater) angle is longer. • Sum of any two sides of a triangle is greater than the third side. • Difference of any two sides of a triangle is smaller than the third side.
  • 23. Some Facts About Triangles. 7
  • 24. Centres of a circle • Incentre- The three angle bisectors of a triangle meet in one point called the incentre. It is the centre of the incircle, the circle inscribed by the triangle
  • 25. • Circumcentre- Three perpendicular bisectors of the sides of the triangle meet in one point called circumcentre. It is the centre of the circumcircle, the circle circumscribed about the circle.
  • 26. • Centroid- The three medians meet in the centroid of the centre or center of the mass(centre of gravity).
  • 27. • Orthocentre- The three altitudes of a tiangle meet in one point called the orthocentre.
  • 28. PYTHAGORAS EUCLID PASCAL MATHEMATICIANS RELATED TO TRIANGLES
  • 29. GUNNEEK, ARSDEEP, NIDHI & ANJALI