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Hi do you mind explaining?

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Usually, I would teach congruence and similarity with lots of visual aid since it requires some visualisation but I will try my best to explain in text.

First, let’s revise the concepts of congruence and similarity. When we say two figures are congruent, we mean that all its corresponding sides and angles are equal. Basically, they are identical.

When we say two figures are similar, what we mean is that the every single side of the figure is either increased or decreased by a common factor. For example, if I have a triangle with sides, 4cm, 8 cm, and 12 cm. I would expect a similar triangle to have the corresponding side lengths of 2cm, 4cm, and 6cm. The common factor or scale factor in this case is 1/2 for all sides.

In the case of the figures in the questions, they are rectangles. This means that the length of rectangle IJKL (36cm) when divided by a common factor will give me the length of rectangle MNPQ (x+6 cm). Similarly, if i take the breath of rectangle IJKL (24cm) and divide it by this common factor, it will give me the breath of rectangle MNPQ (x cm).

Since the scale factor is the same, we can come up with the following equation:

Length of rectangle IJKL / Length of rectangle MNPQ = Breath of rectangle IJKL / Breath of rectangle MNPQ 

So… 36 / (x+6) = 24 / x

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