Interactive simulation - Types of Triangles and proof

🔺 TRIANGLE LEARNING LAB

Explore triangles and discover why the sum of their interior angles is 180°.

Learning Outcomes

• Identify triangles based on their sides.
• Identify triangles based on their angles.
• Understand the properties of an equilateral triangle.
• Investigate the sum of three interior angles.
• Verify the angle-sum property experimentally.

Choose Your Learning Activity

1. Types of Triangles

Explore the Triangle

Angle A: 60° Angle B: 60°

Equilateral Triangle

Remember: An equilateral triangle has three equal sides and three angles of 60° each.

2. Experimental Proof: Sum of Interior Angles

Move the sliders and observe how the three angles change. Their sum remains 180°.

Angle A: 60° Angle B: 60°

60° + 60° + 60° = 180°

Verified: 180°

Geometrical Proof

Step 1: Draw any triangle ABC. Step 2: Extend side BC through C to form a straight line. Step 3: Draw a line through A parallel to BC. Step 4: By alternate interior angles, the angles formed at A on the straight line are equal to angles B and C respectively. Step 5: Angles on a straight line add up to 180°. Therefore,

∠A + ∠B + ∠C = 180°

Special observation: When all three angles are 60°, the triangle is equilateral because all three sides are equal.

Test Your Understanding

1. What is the sum of the interior angles of a triangle?

2. A triangle has three angles of 60°. What is its classification?

Conclusion

The sum of the three interior angles of every triangle is 180°. A triangle with three equal angles of 60° is an equilateral triangle, and all its three sides are equal.