Answers:
B) HL
C) SAS
F) SSS
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Explanations:
The following letters A, L, H, S are defined to be
A = angle
L = leg
H = hypotenuse
S = side
So this means,
HA = hypotenuse angle
HL = hypotenuse leg
AAS = angle angle side
SAS = side angle side
SSS = side side side
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For choice A, we need a pair of hypotenuses to be congruent and a pair of angles to be congruent as well. The pair of angles must be acute (we can't use the right angles). We have tickmarks showing BC = EF, which gives us the knowledge the hypotenuses are congruent. However, we don't have any info about whether any pairs of acute angles are congruent. So we don't have enough info to use HA. Choice A is ruled out.
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Choice B. We can use HL because we know that the pair of hypotenuses is BC = EF shown by the three tickmarks, and we also know that a pair of legs are also congruent (either AB = ED or AC = DF). This is one of the answers.
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Choice C is also an answer. Why? Because we have info about 2 pairs of sides with an included pair of angles. The angle is between the two sides. In this case, AB = ED is one pair of sides, the included angle is A = D, and the other pair of sides are AC = DF.
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Choice D can be ruled out for similar reasons as choice A. We don't have any info about the acute angles.
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Choice E is a similar story. While we have info about one pair of angles,we dont have any info about another pair. The two "A" letters indicates we need info about 2 pairs of angles. Cross choice E off the list.
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Finally, choice F is an answer because we have info about the three pairs of sides. The tickmarks tell us which sides pair up and are congruent.
AC = DF because of the single tickmarks they share together
AB = DE because of the double tickmarks they share together
BC = EF because of the triple tickmarks they share together
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So in summary, the three answers are
B) HL
C) SAS
F) SSS
