Question Bank
QB1:
Do the same three sides always make the same triangle?
QB1A:
A tri1angle is uniquely described by the three sides that it is made out of. This means that
it doesn’t matter how the three sides are put together it will always make the same
triangle. It may be rotated a little bit or flipped over the wrong way, but the triangles are
still equal to each other.
QB2:
Using uncooked spaghetti, try making a triangle with the following side lengths: a = 4cm,
b = 14cm, and c = 8cm. What happens? Can you find different numbers that make the
same thing happen (you may want to write them down on paper)? Why is this happening?
Start keeping a record of the numbers that produce the same error. Try to record the
numbers in some sort of order and see if you can spot a pattern.
QB2A:
Not every combination of three sides will make a triangle. There is a basic property of the
triangle that must not be broken. It is called the triangle inequality property and it states
that the longest side cannot be longer than the two shorter sides added together. This is
because the two shorter sides added together is as far as they can reach if they are put
end-to-end. If the longest side is longer than this then the triangle cannot be constructed.
QB3:
What happens if all three sides are the same length? Is this always true?
QB3A:
If all three sides are equal then an equilateral triangle will be formed. An equilateral
triangle will always be formed if all three sides are the same length.
QB4:
What happens if two sides are the same length? Is this always true? Does it matter which
two sides are the same length?
QB4A:
If two of the sides are equal then the triangle that is formed is called an isosceles
triangle. This will always happen, and it doesn’t matter which two sides are the same
length.
QB5:
Make a triangle with lengths 3cm, 4cm, and 5cm. What do you notice? Can you make a
triangle that is similar?
1
Tri- is a prefix that means three. Think of words like tricycle, tripod, triathlon, and triceratops and you
will see how they get their name too.
QB5A:
A special triangle occurs if one of the interior angles is 90o. This is called a right
triangle. One right triangle can be created by choosing sides of length 3-4-5. Choosing
sides of lengths 6-8-10 (doubling 3-4-5) or 9-12-15 (tripling 3-4-5), can also produce a
right triangle. There are ways to produce a right triangle2 where all the sides are not
whole numbers.
QB6:
A triangle with sides of length 3cm, 4cm, and 5cm is an example of a right triangle3. How
many right triangles can you construct if no side is to be greater than 50cm?
QB6A:
New right triangle triples can be found by doubling, tripling, etc. an old right triangle
triple.
3-4-5
5-12-13 7-24-25 9-40-41
6-8-10 10-24-26 14-48-50
9-12-15 15-36-39
12-16-20
15-20-25
18-24-30
21-28-35
24-32-40
27-36-45
30-40-50
QB7:
Can you make a right triangle with two sides the same length? Can you make another
one?
QB7A:
If the equal sides have a length of 1 then the longest side will have a length of
approximatelly1.4. If the equal sides have a length of 3 then the longest side will have a
length of approximately 3 x 1.4. This is called a right isosceles4 triangle.
QB8:
What are the three types of triangles? How are they different?
QB8A:
The three types of triangles are scalene, isosceles, and equilateral. They are different in
that each one has a different number of equal sides. The scalene triangle has no sides
equal, the isosceles has two equal sides, and the equilateral has all sides equal.
2
Link to a lesson on right triangle from grade 6, 7, or 8.
Link to definition in the Learn window.
4
Link to a lesson right isosceles triangles from grade6,7, or 8.
3
QB9:
Is every equilateral triangle isosceles? Why or why not?
QB9A:
Every equilateral triangle is isosceles. For a triangle to be isosceles it must have two
equal sides, and an equilateral triangle does have two equal sides (in fact it has three).
QB10:
Is every isosceles triangle equilateral? Why or why not?
QB10A:
Not every isosceles triangle is equilateral. Most isosceles triangles don’t have all three
sides equal, and that is the requirement for an equilateral triangle.
QB11:
In an isosceles triangle, can any two angles be equal or does it depend on which sides are
equal?
QB11A:
It depends on which sides are equal, because the length of the sides of a triangle
determine the angles between the sides.
QB12:
What is a right triangle?
QB12A:
A right triangle is one that contains a right angle. When two sides of the triangle meet in
an “L” shape, we have a right (or 90 degree) angle.
QB13:
Where in the physical world can you find triangles? Can you see any right now?
QB13A:
Triangles often appear in architecture. Bridges and skeletons of office buildings are often
made up of triangles. This is because a triangle is one of the strongest figures. Parts of
houses are also often triangular. Look at a roof; how many triangles can you see? Think
about the pyramids in ancient Egypt as well. All of the faces of the pyramids are
triangular. Sometimes triangles are not so obvious to spot. When you lean a ladder
against a wall a triangle is formed. Look at a bicycle. The frame usually has triangular
sections. What about when you put your hand on your hip? A triangle is formed
between the side of your body and your upper and lower arm. Below are some more
examples of triangles in the real world.
QB14:
Can a right triangle be equilateral? Why or why not?
QB14A:
A right triangle cannot be equilateral. A requirement for right triangles is that they must
have one longest side.
QB15:
State the triangle inequality.
QB15A:
The longest side of a triangle cannot be longer than the two shorter sides added together.
This is because the two shorter sides added together is as far as they can reach if they are
put end-to-end. If the longest side is longer than this then the triangle cannot be
constructed.
QB16:
Can an equilateral triangle fail the triangle inequality? What about an isosceles triangle?
Explain.
QB16A:
An equilateral triangle cannot fail the triangle inequality because all three sides of the
triangle must be equal. This means that one side cannot possibly be longer than the other
two sides added together. An isosceles triangle can fail the triangle inequality. Take for
example a triangle of side lengths 4cm, 4cm, and 10cm. There are two equal sides, but
the triangle cannot be constructed.
QB17:
How many triangles can you find in the figure below?
QB17A:
There are a total of 35 triangles in this picture.