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 TriangleThree equal sides | |
Isosceles TriangleTwo equal sides | |
Scalene TriangleNo equal sides |
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 TriangleAll angles are less than 90° | |
Right TriangleHas a right angle (90°) | |
Obtuse TriangleHas an angle more than 90° |
Combining the Names
Sometimes a triangle will have two names, for example: Right Isosceles TriangleHas a right angle (90°), and also two equal angles |
Play With It ...
Try dragging the points around and make different triangles:
You might also like to play with the Interactive Triangle.
Angles
The three interior angles always add to 180°
Perimeter
The perimeter is the distance around the edge of the triangle: just add up the three sides:
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":
(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.