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.