Emily-Jane Bray
2021-02-26
Ian Adams
Skilled2021-04-16Added 160 answers
Triangle = Figure with three sides. Study the following triangle: A,B,C to points. a, b, c to sides. x, y, z to angles.
Perimeter of triangle = a + b + c
Remember that, Sum of all the angles is always
i.e. x + y + z =
Basically there are three types of triangles excluding right angle triangle. Let me tell you how they vary from each other.
Scalene Triangle: No side of triangle is equal.
Isosceles Triangle: Two sides of triangle are equal.
Equilateral Triangle: All sides of triangle are equal.
Scalene | Isosceles | Equilateral | |
Definition | a ne b ne c | ane b = c | a = b = c |
Area | A | ||
Height | - |
where, s = (a+ b+ c)/2
1. Sum of all exterior angles is
Study the following set of triangles and their exterior angles,
a, b, c to Interior angles. p, q, r and s, t, u to Exterior angles.
So, sum of exterior angles =
2. Next property of exterior angle which is important in paper point of view:
External angle = Sum of two internal angles.
For example: In above figures,
r = a + b
q = a + c
s = b + c and so on.
Following triangle is a right angle triangle i.e. a triangle with one out of three 90^o angle.
Area = 1/2 times Base times Perpendicular
Example: In following figure, CE is perpendicular to AB, angle ACE = 20^o and angle ABD = 50^o. Find angle BDA:
Solution: To Find: angle BDA
For this what we need --- angle BAD Because, Sum of all angles =
Consider, triangle ECA,
CEA + EAC + ACE =
Now, come to triangle ABD,
ABD + BDA + BAD =
Example: In given figure. BC is produced to D and angle BAC =
Solution: In above figure, ACD is an exterior angle, and according to property, Exterior angle = Sum of interior angles Therefore, ACD =
This is not the end of this chapter. These are just the basics. In next session, I will discuss some important results, properties (congruency, similarity) and much more. Always remember, Geometry needs practice and time.