triangles

1. Triangles
(Important Points)
Lecture 1

2.  Incentre
 Centroid
 Orthocenter
 Circumcentre
Important Points of Triangles

3.  Intersection point of angle bisectors of triangle is called incentre of
triangle.
Incentre of Triangle
I
A
C B
Incentre

4. Position of Incentre

5. Formula of Inradius

6. Median

7.  Intersection point of Medians of triangle is called Centroid of triangle.
Centroid of Triangle
G
A
C B
Centroid

8. Q. In the given fig. ABCD is a parallelogram. E is any point on diagonal AD. If
area of ∆ BED is 19.5 cm2 , AD= 10 cm and DC= 5 cm. Find the area of
∆ CED.
Sol.
Solved Example

9. Position of Centroid

10.  Centroid divide the median in 2:1
 Centroid divide the triangle into three tingles of equal area.
Ar. Of ∆AGB= Ar. Of ∆AGC= Ar. Of ∆BGC
 All median divide the triangle into six triangles of equal area.
Note

11. Q. In given ABC, AD and BE are medians of triangle which intersect each
other at point G. If area of triangle BDG is 1 cm2, then what is the area of
DCEG? [Rajasthan NTSE Stage-1 2018]
(A) 2 cm2 (B) 3 cm2 (C) 4 cm2 (D) 1 cm2
Solved Example

12. Area of triangle if length of Medians are Given

13.  Let the length of medians of triangle is a, b, c, then area of triangle will be:
Area=
4
3
𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐)
s=
𝒂+𝒃+𝒄
𝟐
Note

14.  Intersection point of Altitudes of triangle is called Orthocentre of triangle.
Orthocentre of Triangle
O
A
C B
Orthocentre

15. Position of Orthocentre

16. Conclusion

17. Thank You