Triangles

Triangles

1. A triangle is a closed figure formed by three intersecting line segments.

2. The sum of all angles of a triangle is 180⁰.

3. On the basis of sides, triangles are classified as equilateral, isosceles and scalene. On the basis of angles, they are classified as right angled, acute angled and obtuse angled triangles.

4. Two triangles are congruent, if and only if one of them can be made to superimpose on the other, so as to cover it exactly.

   • SAS: Two triangles are congruent, if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
   • ASA: Two triangles are congruent if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle.
   • AAS: Two triangles are congruent if two angles and any side of one triangle are equal to two angles and the corresponding side of the other triangle.
   • SSS: Two triangles are congruent if three sides of one triangle are respectively equal to three sides of the other triangle.
   • RHS: Two right triangles are congruent if the hypotenuse and one side of one triangle are equal (respectively) to the hypotenuse and one ccorresponding side of the othher triangle.

5. Angles oppossite to equal sides of a triangle are equal and vice versa.

6. Each angle of an equilateral triangle is equal to 60 degrees.

7. If the altitudes of a triangle are equal, then it is an equailteral triangle.

8. In a triangle, angle opposite to the longer side is greater and side opposite to the greater angle is longer.

9. Sum of any two sides of a triangle is greater than the third side.

10. The difference of any two sides of a triangle is less than the third side.

11. From all of the line segments that can be drawn too a given line, from a point not lying on it, the perpendicular lline segment is the shortest one.