Geometry (Triangle Basic Concepts)

Obtuse (one angle is more than 90°).

Angle opposite to the larger side is always greater than angle opposite to smaller side.

Sum of two sides is greater than third.

So, in a trianlgle ABC
AB + BC > AC,
AB + AC > BC
And AC + BC > AB

For acute angle triangle: AB² + BC² > AC², AB² + AC² > AB² and BC² + AC² > AB²

For right angle triangle: AB² + BC² = AC², where AC is hypotenuse

For obtuse angle triangle: AB² + BC² < AC², where AC is the largest side

There is one more way of classifying the triangles as:

i. Scalene (none of the sides are equal), Isosceles (two sides are equal) and equilateral triangle (all of the sides are equal).

ii. Congruency of triangles: Two or more triangles are congruent when they are equal in all aspects (shape, size and everything).

Conditions for congruency:
i) SSS congruency: When all the sides of the given two or more triangles are equal, then the triangles are congruent.

ii) SAS congruency: When two sides of the given two or more triangles are equal and angle formed by these two sides are also equal, then also the two triangles are congruent.

iii) ASA congruency: When two angles of the given two or more triangles are equal and side between these two angles are also equal, then also the two triangles are congruent.

iv) RHS congruency: If in two or more triangles we have right angle, equal hypotenuse and one of the other sides also equal, then the triangles will be congruent.