Is an equilateral triangle scalene or isosceles?

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Is an equilateral triangle scalene or isosceles?

Is an equilateral triangle scalene or isosceles?
 

A triangle has three sides and three angles

Is an equilateral triangle scalene or isosceles?
 

The three angles always add to 180°

Equilateral, Isosceles and Scalene

There are three special names given to triangles that tell how many sides (or angles) are equal.

There can be 3, 2 or no equal sides/angles:

Equilateral Triangle

Three equal sides
Three equal angles, always 60°

Isosceles Triangle

Two equal sides
Two equal angles

Scalene Triangle

No equal sides
No equal angles


How to remember? Alphabetically they go 3, 2, none:

  • Equilateral: "equal"-lateral (lateral means side) so they have all equal sides
  • Isosceles: means "equal legs", and we have two legs, right?   Also iSOSceles has two equal "Sides" joined by an "Odd" side.
  • Scalene: means "uneven" or "odd", so no equal sides.

What Type of Angle?

Triangles can also have names that tell you what type of angle is inside:

Acute Triangle

All angles are less than 90°

Right Triangle

Has a right angle (90°)

Obtuse Triangle

Has an angle more than 90°


Combining the Names

Sometimes a triangle will have two names, for example:

Right Isosceles Triangle

Has a right angle (90°), and also two equal angles

Can you guess what the equal angles are?

Play With It ...

Try dragging the points around and make different triangles:

geometry/images/triangle.js?mode=type

You might also like to play with the Interactive Triangle.

Angles

The three interior angles always add to 180°

geometry/images/triangle.js?mode=angles

Perimeter

The perimeter is the distance around the edge of the triangle: just add up the three sides:

geometry/images/triangle.js?mode=perim

Area

The area is half of the base times height.

  • "b" is the distance along the base
  • "h" is the height (measured at right angles to the base)

Area = ½ × b × h

The formula works for all triangles.

Note: a simpler way of writing the formula is bh/2

Example: What is the area of this triangle?

(Note: 12 is the height, not the length of the left-hand side)

Height = h = 12

Base = b = 20

Area = ½ × b × h = ½ × 20 × 12 = 120

The base can be any side, Just be sure the "height" is measured at right angles to the "base":

geometry/images/triangle.js?mode=area

(Note: You can also calculate the area from the lengths of all three sides using Heron's Formula.)

Why is the Area "Half of bh"?

Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (a parallelogram) which can be changed to a simple rectangle:

THEN the whole area is bh, which is for both triangles, so just one is ½ × bh.

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Is an equilateral triangle An scalene triangle?

There are three types of triangle based on the length of its sides: Equilateral triangle: All sides are equal in length. Isosceles triangle: Two sides are equal in length. Scalene triangle: All sides have different lengths.

Is a equilateral triangle an isosceles triangle?

An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. Another special case of an isosceles triangle is the isosceles right triangle.

How can you tell if an equilateral isosceles or scalene?

A triangle is scalene if all of its three sides are different (in which case, the three angles are also different). If two of its sides are equal, a triangle is called isosceles. A triangle with all three equal sides is called equilateral.

Is an equilateral triangle always scalene?

If two are of the same length and different from the third side, it's neither equilateral nor scalene triangle. For instance, a triangle with side lengths of 3 , 4 and 5 (in some measurement units) is a scalene triangle, but that with length 4 , 4 and 5 is not.