Question

I need help with three questions please :-)

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Answer 1

1. No, ... not similar ... segments are not proportional
2. ∠A ≅ ∠Y
3. AB/A"B" = BC/B"C"

Explanation:

1. The side length ratios are ...

AB : BC : CD = 2 : √5 : 4

and

EF : FG : GH = 4 : √10 : 6

Corresponding segments are not proportional, so the figures cannot be similar.

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2. The problem statement tells you the corresponding vertices are (B, X), (A, Y), (C, Z). You know this because the names of the similar figures are given as ΔBAC and ΔXYZ and corresponding vertices are listed in the same order. The angles at corresponding vertices of similar figures will be congruent. The only pair listed among the answer choices is ...

∠A ≅ ∠Y

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3. In similar figures, corresponding segments have the same ratio (the dilation factor). This means, for example, that

A"B" = 3AB and B"C" = 3BC

so an appropriate proportionality statement is ...

AB/A"B" = BC/B"C"