Download Let`s Learn About Triangles!

Let’s Learn About Triangles!
There’s no need to be scared of triangles –
they make sense if you take the time to get to know them!
EQUILATERAL TRIANGLE
An equilateral triangle is one in which all sides are equal and all angles are equal. In a triangle of any size or
shape, the sum of all the angles is 180 degrees. So in an equilateral triangle, each angle must be 60 degrees (3
angles x 60 degrees each = 180 degrees total).
60°
60°
60°
RIGHT ANGLED TRIANGLES
A right angled triangle has one right angle
(an angle that is 90 degrees). The other two angles can be
any size. Here are some examples of right angled triangles. Find the right angle in each triangle and circle it:
OBTUSE ANGLED TRIANGLES
An obtuse angled triangle has one angle that is greater than 90 degrees.
Find the obtuse angle in each triangle and circle it:
ISOSCELES TRIANGLE (“eye-soss-ul-eez”)
An isosceles triangle is one in which two angles and two sides are identical.
In each triangle below, find the two identical angles and circle them:
SCALENE TRIANGLE (“skay-leen”)
A scalene triangle is one in which all the angles are different and all the sides are different. The angles can
include obtuse, acute and right angles, but all the angles must be different for the triangle to be scalene.
Three of the triangles below are scalene. Find them and mark all of the angles in each scalene triangle with a
cross (you may need to use a protractor to be sure! Fun!):
ACUTE ANGLED TRIANGLE
An acute angled triangle is one in which all of the angles are less than 90 degrees. Find all four acute angled
triangles below and circle them:
Combining these terms
You can combine these terms when naming your triangle, but only in ways that make sense.
For example, you can have an obtuse angled isosceles triangle. It looks like this:
It’s obtuse angled because one angle is more than 90 degrees.
It’s isosceles because the other two angles are identical.
But could you have an obtuse angled equilateral triangle? No, because the obtuse angle has to be more than
90 degrees, and we know that in an equilateral triangle all the angles must be 60 degrees. These two concepts
are incompatible. An obtuse angled equilateral triangle cannot exist.
Possible or Impossible?
Using what you’ve learned, decide whether the following triangles are possible or impossible:
1)
2)
3)
4)
5)
6)
7)
8)
9)
Obtuse angled equilateral triangle
Acute angled isosceles obtuse angled triangle
Right angled scalene triangle
Right angled obtuse angled triangle
Obtuse angled scalene triangle
Acute angled isosceles triangle
Acute angled equilateral triangle
Right angled equilateral triangle
Equilateral triangle
possible
possible
possible
possible
possible
possible
possible
possible
possible
impossible
impossible
impossible
impossible
impossible
impossible
impossible
impossible
impossible
NAME THAT TRIANGLE AND EXPLAIN WHY!
90°
For each triangle, name it, and write down your reasoning.
Here’s an example answer for a right-angled isosceles triangle:
“Because one angle is 90 degrees, which means that it’s right angled,
and the other two angles are identical, which means it’s isosceles”.
Equal angles
Name of Triangle:
Why:
Name of Triangle:
62°
Why:
70°
48°
Name of Triangle:
Why:
Name of Triangle:
Why:
Name of Triangle:
Why:
Name of Triangle:
Why:
Name of Triangle:
Why:
The best way to learn something is to teach it to someone else!
Find a friend to work with, and teach them each of these triangles.
Be sure to explain why: “It’s a right angled, because one of the angles is 90 degrees, and
it’s isosceles, because the other two angles are identical, so it’s a right angled isosceles
triangle”. Then have them teach it to you! If you can’t eyeball the angles to determine
what kind of triangle you’re looking at, then use a protractor. Have fun!