Triangle Important Properties.docx

1. SINE RULE Sin A/a = Sin B/b = Sin C/c

2. EQUILATERAL TRIANGLE  r = H/3 = a/2 3  R = 2H/3 = a/ 3  R = 2r  Area ( circumcircle) = 4 * Area (incircle)  From a point inside eq. triangle, perpendiculars p1, p2, p3 dropped on three sides, then

altitude or height of triangle = p1 + p2 + p3 or p1+ p2+ p3 = 3/2 a 3. RIGHT ANGLED TRAINGLE  R (circumradius) = median to hypotenuse = hypotenuse/ 2  r ( inradius) = a+c-b/ 2  h (height or altitude ) = ac/b or h=mxn

 For right Triangle of 3,4,5 R= 2.5 and r = 1 Similarly For any 3x, 4x, 5x right triangle, R= 2.5x and r= x  TRIPLETS: 5, 12, 13

7, 24, 25

9, 40, 41

11, 60, 61

13, 84, 85

8, 15, 17

12, 35, 37

16, 63, 65

20, 21, 29

38, 56, 65 4. ISOSCELES TRAINGLE  area = b/4 4a – b  Bisector of angle A is perpendicular to the base and also median to base.  Isosceles right triangle Area= legs / 2 Or Area= hypotenuse / 4

5. IMPORTANT POINTS Medians : CENTROID

( 2 : 1)

Perpendicular Bisectors : CIRCUMCENTRE

R= abc/ 4 x area

( any point on perpendicular bisector is equidistant from the ends of the line) Angle Bisectors : INCENTRE

r = area/ semi p

( incentre divides the bisector of angle A in ratio b+c/ a ) Perpendiculars or altitudes : ORTHOCENTRE

6. SIMILAR TRAINGLES

 Ratio of sides = ratio of heights = ratio of medians = ratio of angle bisectors = ratio of in radius = ratio of circumradius  Ratio of areas = ratio of squares of corresponding sides