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Triangles

Triangle with angles

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A triangle has three sides and three angles
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The iii angles always add together 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 exist 3, 2 or no equal sides/angles:

Equilateral Triangle

Equilateral Triangle

Three equal sides
Three equal angles, always 60°
Isosceles Triangle

Isosceles Triangle

2 equal sides
Ii equal angles
Scalene Triangle

Scalene Triangle

No equal sides
No equal angles

How to remember? Alphabetically they get three, 2, none:

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

What Type of Angle?

Triangles tin can also have names that tell y'all what blazon of angle is within:

Acute Triangle

Acute Triangle

All angles are less than xc°
Right Triangle

Right Triangle

Has a right angle (90°)
Obtuse Triangle

Birdbrained Triangle

Has an angle more than 90°

Combining the Names

Sometimes a triangle volition take ii names, for example:
Right Isosceles Triangle

Right Isosceles Triangle

Has a correct angle (90°), and also ii 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=blazon

You might also like to play with the Interactive Triangle.

Angles

The three interior angles ever 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?style=perim

Area

triangle base=b height=h

The area is one-half of the base times top.

  • "b" is the distance forth the base
  • "h" is the meridian (measured at correct angles to the base)

Area = ½ × b × h

The formula works for all triangles.

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

Case: What is the surface area of this triangle?

Triangle height=12, base=20

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

Summit = h = 12

Base of operations = b = 20

Area = ½ × b × h = ½ × twenty × 12 = 120

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

geometry/images/triangle.js?mode=area

(Note: Y'all can besides summate the surface area from the lengths of all 3 sides using Heron'south Formula.)

Why is the Area "Half of bh"?

Imagine you "doubled" the triangle (flip it around one of the upper edges) to brand a square-similar shape (a parallelogram) which can be inverse to a uncomplicated rectangle:

triangle area

And so the whole expanse is bh, which is for both triangles, and so but one is ½ × bh.

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