Triangle ppt
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This document provides an overview of triangles, including definitions, types, properties, secondary parts, congruency, and area calculations. It defines a triangle as a 3-sided polygon with three angles and vertices. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angle measures as acute, obtuse, or right. Key properties discussed include the angle sum theorem, exterior angle theorem, and Pythagorean theorem. Secondary parts like medians, altitudes, perpendicular bisectors, and angle bisectors are also defined. Tests for triangle congruency such as SSS, SAS, ASA, and RHS are outlined. Formulas are provided for calculating the areas of
Triangle ppt
- 1. TRIANGLES
- 2. CONTENTS • TRIANGLES 1. 2. 3. 4. 5. 6. DEFINITION TYPES PROPERTIES SECONDARY PART CONGRUENCY AREA
- 3. TRIANGLES A triangle is a 3-sided polygon. Every triangle has three sides, three vertices and three angles. 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. The study of triangles is sometimes known as triangle geometry and is a rich area of geometry filled with beautiful results and unexpected connections.
- 4. What do these symbols mean? right angle parallel to each other same length as each other parallel to each other, but not parallel with the sides with only one arrow same length as each other, but not the same length as the sides with only one dash
- 6. TYPES OF TRIANGLES 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
- 7. EQUILATERAL TRIANGLE Triangles having all sides equal are called Equilateral Triangle. ISOSCELES TRIANGLE Triangles having 2 sides equal are called Isosceles Triangle.
- 8. SCALENE TRIANGLE Triangles having no sides equal are called Scalene Triangle.
- 9. ACUTE ANGLED TRIANGLE Triangles whose all angles are acute angle are called Acute Angled Triangle. OBTUSE ANGLED TRIANGLE Triangles whose 1 angle is obtuse angle are called Obtuse Angled Triangle. RIGHT ANGLED TRIANGLE Triangles whose 1 angle is right angle are called Right Angled Triangle.
- 11. PROPERTIES OF A TRIANGLE Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise. In rigorous treatments, a triangle is therefore called a 2-simplex. Elementary facts about triangles were presented by Euclid in books 1–4 of his Elements, around 300 BC. The measures of the interior angles of the triangle always add up to 180 degrees.
- 12. PROPERTIES OF A TRIANGLE The measures of the interior angles of a triangle in Euclidean space always add up to 180 degrees. This allows determination of the measure of the third angle of any triangle given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the Exterior Angle Theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.
- 13. 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.
- 14. 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
- 16. MEDIAN OF A TRIANGLE The Line Segment joining the midpoint of the base of the Triangle is called Median of the Triangle. OR A Line Segment which connects a vertex of a Triangle to the midpoint of the opposite side is called Median of the Triangle. MEDIAN
- 17. ALTITUDE 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
- 18. 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
- 19. ANGLE BISECTOR A line segment that bisects an angle of a triangle is called Angle Bisector of the triangle. ANGLE BISECTOR
- 21. 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.
- 22. 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.
- 23. 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-SideAngle Criteria of Congruency.
- 24. 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 AngleHypotenuse-Side Criteria of Congruency.
- 26. HERON’S FORMULA Heron’s Formula can be used in finding area of all types of Triangles. The Formula is ::-> AREA = S = Semi-Perimeter a,b,c are sides of the Triangle
- 27. FORMULA FOR ISOSCELES TRIANGLE Area of an Isosceles Triangle = b = base a = length of equal sides
- 28. FORMULA FOR RIGHT ANGLED TRIANGLE ½ x base x height
- 29. PYTHAGORAS EUCLID PASCAL MATHEMATICIANS RELATED TO TRIANGLES
- 30. THANKS Made by:Lovish Goyal IX- ‘A’