Understanding Triangles: A Comprehensive Guide to Their Classification and Properties

Step-by-step Guide: Classifying Triangles

Based on Sides:

• Equilateral Triangle:
  • All three sides are of equal length.All three angles measure \(60^\circ\).

  Isosceles Triangle:

  • Two sides are of equal length.The angles opposite these equal sides are also equal.

  Scalene Triangle:

  • No sides are of equal length.None of the angles are equal.

Based on Angles:

• Acute Triangle:
  • All three angles are less than \(90^\circ\).

  Right Triangle:

  • One angle measures exactly \(90^\circ\).

  Obtuse Triangle:

  • One angle measures more than \(90^\circ\).

Examples:

Example 1:
If a triangle has sides measuring \(5 \text{cm}\), \(5 \text{cm}\), and \(7 \text{cm}\), what type of triangle is it?
Solution: The triangle is an Isosceles Triangle since it has two sides of equal length.

Example 2:
Identify a triangle with sides of \(3 \text{cm}\), \(4 \text{cm}\), and \(5 \text{cm}\).
Solution: The triangle is a Scalene Triangle as all its sides have different lengths.

Example 3:
A triangle has angles measuring \(60^\circ\), \(60^\circ\), and \(60^\circ\). What type of triangle is it based on its angles?
Solution: The triangle is an Acute Triangle since all its angles are less than \(90^\circ\).

Example 4:
Identify a triangle with angles of \(90^\circ\), \(45^\circ\), and \(45^\circ\).
Solution: The triangle is a Right Triangle due to the presence of a \(90^\circ\) angle.

Practice Questions:

1. Classify a triangle with angles measuring \(80^\circ\), \(60^\circ\), and \(40^\circ\).
2. What type of triangle has sides measuring \(6 \text{cm}\), \(6 \text{cm}\), and \(6 \text{cm}\)?
3. Identify a triangle with one angle measuring \(100^\circ\) and the remaining two angles totaling \(80^\circ\).

Answers:

1. Acute Triangle.
2. Equilateral Triangle.
3. Obtuse Triangle.