foundations 11

[dusty lava]

You need at least 2 angles to prove by Angle-Angle similarity, only 1 is not enough! So A and B we should eliminate.

For AB/DE=AC/DF, it’s actually usable! All of the sides are corresponding, meaning that they are correctly placed in ratios where they’re opposite of the same angles.

Meaning that for example, AC is opposite to 90* angle, and DF is also opposite to a 90* angle.

DE and AB are also opposite to the same degree angles expressed by “•”, which means that the side of triangles opposite to the said same-degree angle are similar.

So let’s say then, sides opposite to 90* is expressed as “x,”
(AC and DF is then x)

and ones opposite to “•” as “y.”
(AB and DE is then y)

Let’s substitute
AB/DE= AC/DF
x/x = y/y
Which we cancel out the same values…
1/1 = 1/1
This shows that the ratios of corresponding sides of these different triangles result the same output— that is to say, the ratios are the EQUAL!

When ratios of CORRESPONDING sides are equal, that means we have proven their similarity.

Our answer is C.