Question

Given triangle FGH similar to triangle LMN, which must be true? Select all that apply

Answer 1

Answers:

A. True

B. True

C. True

D. False

E. True

In short, only answer choice D is false. Everything else is true.

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Explanations:

A. The ordering of FGH and LMN is important. This is because F and L pair up as the first letters of the triple letter sequences, so do G and M as the second letters. Segment FG pairs up with LM because we're talking about the first two letters of both sequences. At the same time, FH and LN pair up because they are composed of the first and third letters of FGH and LMN respectively. Due to the triangles being similar, we can say FG/LM = FH/LN, ie we have a proportion.

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B. Segment LN is proportional to FH, as explained back in part A. For example, FH could be 10 times longer than LN, making FH = 10*LN. Once the scale factor is set, you must use it for the other pairs of sides as well.

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C. Similar triangles have corresponding angles that are congruent. This means F = L, G = M and H = N. Dividing the measure of F over the measure of L leads to 1 (regardless of what the angles happen to be) due to the rule x/x = 1, where x is nonzero. The same thing happens with dividing the measures of angle G over angle M. We get 1 on both sides after simplifying this given equation, so it is a true equation.

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D. Similar triangles are not congruent, so their corresponding side lengths are not congruent either.

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E. As explained back in part C, the corresponding angles are congruent because we know the triangles to be similar. The ordering of the letters matter. Angles H and N are the third letters of FGH and LMN respectively, which is why they pair up and are congruent.

Answer 2

The correct options are A, B, C and E.

It is given that,

• Triangle FGH is similar to triangle LMN

Explanation:

The triangles FGH and LMN are similar, so their corresponding angles are congruent and corresponding sides are proportional.

$\dfrac{FG}{LM}=\dfrac{FH}{LN}$

It means option A is correct.

$FH\sim LN$

It means option B is correct.

Using the definition of similarity,

$\angle F\cong \angle L,\angle G\cong \angle M,\angle H\cong \angle N$

$\dfrac{m\angle F}{m\angle L}=\dfrac{m\angle G}{m\angle M}=1$

It means option C is correct.

Corresponding sides are similar, not congruent. So, the statement $GH\cong MN$ is false.

It means option D is incorrect.

$\angle H\cong \angle N$

It means option E is correct.

Thus, the correct options are A, B, C and E.

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