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Similar shapes are enlargements of each other using a scale factor!
The corresponding side on shape A is 2 x longer than shape B.
Therefore the shape is similar by a scale factor of 2.
Shapes that are exactly the same shape and size are congruent.
RECAP - Four Rules of Congruency - Triangles
1) Three matching sides (SSS)
2) Two matching sides and the angle between them (SAS)
3) Two matching angles and a corresponding side (AAS)
4) In a right-angled triangle, the hypotenuse and one matching side (RHS)
In this activity, we will answer mixed questions on congruency and similarity!
Let's look at a typical question.
Example
The triangles below are drawn to scale. They are either congruent or similar to A.
State which they are.
If congruent, state the condition and if similar state the scale factor.
Answer
B - This is the same size and shape as A.
It is congruent even though it is a reflection of A.
All three sides are the same SSS
Or we could use RHS as we have a right-angle, hypotenuse and another side the same.
C - Is also congruent to shape A.
It is rotated but still congruent.
As with B we can use the SSS or RHS conditions to state congruency.
D is not the same size as A.
The sides are twice as long (6 ÷ 3 = 2)
So, we can say that shape D is similar by scale factor 2.
Let's try some mixed questions like this!
