Triangles and it's properties

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1. prepared By: minhaj noushad , TRIANGLES AND ITS PROPERTIES

2. INTRODUCTION Polygon Polygon is a simple close curve formed by the line segments is called a polygon. Triangle s a polygon with least number of lines Triangle A plane figure formed by three non parallel line segment is called a triangle Elements of triangle The three sides AB,BC,AC and angle abc ,, angle bac and angle acb denoted by angle a, angle b and angle c together is known as six part of or elements of triangle abc a b c

3. TYPES OF TRIANGLES (BASED ON ITS SIDES)

4. EQUILATERAL TRIANGLE Equilateral triangle: A triangle with three congruent (equal) sides and three equal angles These marks indicate equality . A B C

5. ISOSCELES TRIANGLES At least two sides are the same length 5 A B C

6. SCALENE TRIANGLES Scalene triangle: A triangle that has no congruent (equal) sides A B C

7. TYPES OF TRIANGLES (BASED ON ITS ANGLES )

8. ACUTE ANGLED TRIANGLES Acute triangles have three acute angles 8 A B C

9. RIGHT TRIANGLES Right triangle: Has only one right angle (90 degrees) This box indicates right angle A B C

10. OBTUSE ANGLED TRIANGLES Obtuse triangles have one obtuse angle A B C

11. PROPERTIES OF TRIANGLE

12. ANGLE SUM PROPERTY OF TRIANGLE The sum of the measures of the angles of a triangle is 180°. m ∠A + m ∠B + m ∠C = 180 A B C

13. EXTERIOR ANGLE PROPERTY OF TRIANGLE The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles m ∠1 = m∠2 + m∠3

14. INEQUALITY PROPERTY OF TRIANGLE The sum of any two sides of a triangle is greater than the third side. A B C AB+BC >AC AB+AC>BC AC+BC>AB

15. PYTHAGORAS THEOREM OF TRIANGLE In a right triangle, the square of the longest side is equal to the sum of squares of remaining two sides. A B C ( AC ) 2 = (AB ) 2 + (BC) 2 Hypotenuse 2 = Perpendicular 2 + Base 2 Base Perpendicular Hypotenuse

16. CONGRUENCE OF TRIANGLES

17. CONGRUENT TRIANGLES Congruent means identical. Two triangles are said to be congruent if they have equal lengths of sides, equal angles, and equal areas. If placed on top of each other they would cover each other exactly The symbol for congruence is . For two triangles to be congruent (identical), the three sides and three angles of one triangle must be equal to the three sides and three angles of the other triangle. The following are the ‘ tests for congruency’. a b c x y z

18. CASE 1 Three sides of one triangle = Three sides of the other triangle SSS three side A E B F C D

19. CASE 2 Two sides and the included angle of one triangle = Two sides and the included angle of one triangle SAS (side,angle,side ) A B C D E F

20. CASE 3 One side and two angles of one triangle = One side and two angles of one triangle ASA (ANGLE,SIDE,ANGLE ) A B C D E F

21. CASE 4 A right angle , the hypotenuse and the other side of one triangle=A right angle , the hypotenuse and the other side of one triangle RHS ( RIGHT ANGLE,HYPOTNEUS,SIDE ) A B C D E F

22. AREA OF A TRIANGLE

23. To find the area of a triangle: The height = the perpendicular distance from the opposite vertex to the base h b Area of triangle = ½ h b AREA OF TRIANGLE HERON’S AREA FORMULA

24. THE END THANK YOU ALL