Geometry Course/Polygon/Triangle

Triangle

A triangle is a two dimensional polygon that has three sides and three angles with the total sum of the angles equal to 180^o

Three Points A, B, C

Three sides AB, BC, CA

Three angles $\angle A$ , $\angle B$ , $\angle C$

The sum of Three angles $\angle A+\angle B+\angle C=180^{o}$

Similar and Congruent Triangles

Congruent Triangles

Two Triangles are equal or congruent when

• Two triangles have three sides are equal . Side by Side by Side (SSS)
• Two triangles have two sides and angle in between the sides are equal . Side Angle Side(SAS)
• Two triangles have two angles and the side in between the angles are equal . Angle Side Angle (ASA)

Note that there is no AAA congruence(Angle-Angle-Angle) , because then the sides can be different , making it unequal. It can be similar however.

If you were to transpose one congruent triangle with the other , they would superimpose exactly.

Properties

1. Perimeter
2. Area

Special Types of Triangle

1. Right Triangle
2. Isosceles Triangle
3. Equilateral Triangle
4. Scalene Triangle