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Similar Triangles made easy


There are some quite complicated and unnecessary complexities with Similar Triangles for some students. Let’s try and keep it simple. Look at the two triangles below. They look similar but, first, what do we mean by “Similar”? Similar means that one triangle is an enlargement of another. In other words, one triangle has been scaled up or scaled down in relation to another.

In these two triangles, check the lengths of AB and DE. You will note that the length DE is 1.5 times the length of AB. In other words, the lower (yellow) triangle is the top one enlarged by a scale factor of 3/2 or 1.5. You will note that the angle sizes did not change during the enlargement. In two similar triangles we have two properties:
similar triangles1

1. The angles are the same (called “AAA” for all three angles being the same)

2. The corresponding sides have the same scale factor

That’s all there is to it! So, to find x in the lower triangles simply multiply its corresponding side (in the green triangle) by the amount or scale of enlargement. Therefore, x = 3 x 1.5 or 4.5!

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The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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