First, you need to know a bit about congruence:
Two shapes are congruent if they are exactly the same size, and all their lengths and angles are the same.
And now moving on to similarity!
Two shapes are similar if all angles are the same, and the length of the sides are directly proportional to each other (e.g. the sides of one shape are half that of the other).
In other words, the shapes are in the same ratio but they are different sizes.
Let's try a question on this:
These shapes are similar. Find the length of a) x and b) y
Right, so first we need to find the scale factor (SF) between the first shape (let's call it A) and the second (which is now B).
First we need to look at the shapes and find a side which is labelled on both A and B.
We can see that the side labelled 4cm on A corresponds to the side labelled 8cm on B. This helps us find the scale factor. We simply divide the larger number by the smaller one:
8/4 = 2
The SF is 2, which means any line in B will be twice as long as the same line in A.
Let's start with a). We need to find line x, and we can do this by halfing the corresponding line on shape B, which is 5:
5/2 = 2.5cm
So x is 2.5cm. Now for y.
We find the corresponding line on A (4.5) and this time we multiply by 2:
4.5 x 2 = 9cm
So now we know y is 9cm! There will be more soon on doind this with areas and volumes. In the meantime, try our quiz on this:
Comentarios