Video Transcript
Given the following four shapes,
which two are similar?
To answer this, we can recall that
similar shapes are the same shape but different sizes. For shapes to be similar, they must
have corresponding sides which are in the same proportion. So, let’s take a closer look at our
four shapes. We can see that shape one and shape
three look like they are the same shape. Shapes two and four also look like
these could potentially be similar.
Taking the first pair, shape one
and three, let’s have a look at the sides of this shape. Looking at the base of these
triangles then, labeled eight on shape one and four on shape three, then to go from
shape one to shape three, we would half it. So, we could say that the
proportionality would be multiplying by a half. This is the same as dividing by
two.
We now need to check if this
proportionality works for all sides. Taking our vertical side, we can
see that if we take six and multiply by half, we would indeed get three. Taking our final length in, we’re
looking at 10 and thinking if we half it, would we get five? And the answer is yes. This means that all the
corresponding sides are in the same proportion. Therefore, shape one and shape
three are similar.
We can now check if shape two and
shape four are also similar. Starting with the base of these
triangles, then to go from five to eight, we would need to multiply by eight and
then divide by five, which is the same as multiplying by eight over five.
We now need to check if this
proportionality works for the remaining two sides. Comparing the lengths of seven and
12, then we need to check if seven times eight over five equals 12. To calculate seven times eight over
five, we can write our seven as a fraction over one and multiply the numerators and
denominators, which gives 56 over five. As a mixed-number fraction, this
would be equal to 11 and one-fifth. Therefore, seven times eight-fifths
does not equal 12, and so our proportionality does not work. So, shape two and shape four are
not similar.
Therefore, our final answer for the
two similar shapes are shape one and shape three.
