Choose the correct correspondence

Mathematics

1 answer:

STALIN [3.7K]4 years ago

5 0

Answer:

Step-by-step explanation:

Looking at triangles ABD and ACD, they appear to be congruent. This means they have corresponding or matching parts which are equal and form each triangle.

The segment AD is the longest segment of triangle ABD. It matches to the longest segment in ACD. This is the same segment AD since the triangles share a side between them.

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If LR = 12 and LP = 7, find PR. Explain.

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Answer:

PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution

Step-by-step explanation:

The naming of the segments suggests that point P is between L and R, so that ...

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This corresponds to the last choice.

_____

<em>Comments on the alternate interpretation</em>

On the other hand, if point L is between P and R, then the segments are PL and LR. The Segment Addition Postulate would tell you that ...

PL + LR = PR

The Reflexive Property of Congruence would tell you that PL = LP. The Substitution Property would tell you LP can be substituted into this equation, making it ...

LP + LR = PR

and by the commutative property, ...

LR + LP = PR.

Multiple properties of addition and congruence are involved with this interpretation, which more or less matches the third choice. That is, the simple explanation of answer choice 3, by itself, is insufficient to explain why the length of PR should be considered to be 19, not 5.

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