Triangles - Equilateral, Isosceles And Scalene - Math Is Fun

c2ZWPA3kduw Triangles

	A triangle has three sides and three angles
	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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