Triangles JEE NOTES SCALENE ISOSCELES

What is a Triangle?

• A triangle is a closed figure with three sides and three angles.

• The sum of all three angles in a triangle is always 180°.

• Triangles are the simplest polygon.

2. Types of Triangles (Based on Sides)

1. Equilateral Triangle

   • All three sides are equal.

   • All angles are equal (60° each).

2. Isosceles Triangle

   • Two sides are equal.

   • The angles opposite the equal sides are equal.

3. Scalene Triangle

   • All sides are different.

   • All angles are also different.

3. Types of Triangles (Based on Angles)

1. Acute Triangle → All angles less than 90°

2. Right Triangle → One angle is 90°

3. Obtuse Triangle → One angle is greater than 90°

4. Important Concepts

1. Altitude (Height):

   • A line drawn from a vertex perpendicular to the opposite side.

2. Median:

   • A line drawn from a vertex to the midpoint of the opposite side.

3. Angle Bisector:

   • A line that divides an angle into two equal angles.

4. Perimeter:

   • Total length of all three sides of the triangle.

5. Area (Conceptual):

   • Amount of space covered inside the triangle.

5. Important Properties

1. Sum of angles = 180°

2. Longest side lies opposite the largest angle

3. Shortest side lies opposite the smallest angle

4. The triangle inequality principle:

   • The sum of any two sides of a triangle is always greater than the third side

6. Key Points for Exams

• Triangles are classified by sides: equilateral, isosceles, scalene.

• Triangles are classified by angles: acute, right, obtuse.

• Concepts: altitude, median, angle bisector, perimeter, area.

• Properties: sum of angles, side-angle relationship, triangle inequality.