Answers:
A) HL
B) SAS (I'm assuming you meant to say SAS instead of AS)
C) SSS
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Explanation:
The square angle marker tells us we have 90 degree angles. So these are right triangles.
Because we're dealing with right triangles, we could use HL which stands for "hypotenuse leg". The hypotenuse is AR for either triangle, and you could use either of these two pairs for the leg
- AB = AC (one possible pairing), or,
- BR = CR (another possible leg pairing)
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The tickmarks tell us which sides are the same length. We can see that
- AB = AC (single tickmark)
- BR = CR (double tickmarks)
We also know that angle ABC = angle ACR because all right angles are congruent. These facts allow us to use SAS (side angle side). I'm assuming you meant to say "SAS" instead of "AS" for choice B.
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SSS stands for "Side Side Side". It means if we know that three pairs of sides are congruent, then we can prove the triangles congruent overall.
The three pairs of congruent sides are:
- AB = AC (single tickmark)
- BR = CR (double tickmarks)
- AR = AR (shared overlapped side; reflexive property)
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Side notes:
- We can rule choice D out because we don't have enough info to use ASA. We would need info about another pair of congruent angles.
- Similarly, AAS can't be used either. We only have info about one pair of angles (not two). So we can rule out choice E.
