Triangle Classification: Identifying a Shape with Three 60° Angles

Triangle Classification with Equal Angle Measures

What kind of triangle is the following

606060606060606060AAABBBCCC

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Step-by-step video solution

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00:00 Identify which type of triangle it is
00:03 All angles are equal to 60
00:11 In a triangle, equal sides are opposite to equal angles
00:15 Since all angles are equal, all sides are also equal
00:20 Here is the solution

Step-by-step written solution

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1

Understand the problem

What kind of triangle is the following

606060606060606060AAABBBCCC

2

Step-by-step solution

Since in the given triangle all angles are equal, all sides are also equal.

It is known that in an equilateral triangle the measure of the angles will always be equal to 60° since the sum of the angles in a triangle is 180 degrees:

60+60+60=180 60+60+60=180

Therefore, it is an equilateral triangle.

3

Final Answer

Equilateral triangle

Key Points to Remember

Essential concepts to master this topic
  • Rule: All angles equal 60° means all sides are equal
  • Technique: Check angle sum: 60° + 60° + 60° = 180°
  • Check: Equal angles always create an equilateral triangle ✓

Common Mistakes

Avoid these frequent errors
  • Confusing equilateral with isosceles triangles
    Don't call it isosceles when all three angles are 60° = wrong triangle type! Isosceles has only two equal angles/sides. Always remember that three equal angles means equilateral triangle.

Practice Quiz

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Is the triangle in the drawing a right triangle?

FAQ

Everything you need to know about this question

Why are all the angles exactly 60° in an equilateral triangle?

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In any triangle, all angles must add up to 180°. If all three angles are equal, then each one must be 180°3=60° \frac{180°}{3} = 60° !

How is an equilateral triangle different from an isosceles triangle?

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Equilateral: All 3 sides equal, all 3 angles = 60°

Isosceles: Only 2 sides equal, only 2 angles equal (not 60°)

Can a triangle have three 60° angles but different side lengths?

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No! If all angles are equal, then all sides must be equal too. This is a fundamental property of triangles - equal angles create equal opposite sides.

What if I see a triangle that looks equilateral but angles aren't marked?

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Look for tick marks on the sides! Three identical tick marks mean all sides are equal, so it's equilateral. You can also measure if needed.

Are there any other special properties of equilateral triangles?

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  • All sides equal
  • All angles = 60°
  • Three lines of symmetry
  • All altitudes, medians, and angle bisectors are the same

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