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# ​ABC∼PQR Which statements are true?

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Thank you

Johnnyboy  Dec 1, 2017
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#1
+91786
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The 1st, 3rdand 5th are correct.

I'm not sure what the difference in notation means for the 2nd and 4th

[maybe someone knowledgable would like to fill me in?]

but none of the side lengths will (necessarily) be equal.

Melody  Dec 1, 2017
#2
+82859
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These symbols often confuse me, too.....

The second one says that AC is congruent to PR....however....the triangles are similar, not congruent, so this is false....for the same reason, the fourth one is also false....the triangles would have to be congruent for BC = QR

CPhill  Dec 1, 2017
#3
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Thanks Chris but I still do not know the relevance of the overbar...

Melody  Dec 1, 2017
#4
+1714
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To reference segments as figures, it is considered standard to use an overbar to make this clear.

$$\overline{AB}$$ means a segment

$$AB$$ means the length of the segment.

Get it?

TheXSquaredFactor  Dec 1, 2017
#5
+91786
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Thanks xsquared,

but what does

$$\overline{AB}\cong\overline{PR}$$

Actually mean?

I mean if it is not referring to their lengths, what is it referring to?

Melody  Dec 2, 2017
#6
+1714
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It is referring to the figures themselves--not their lengths.

$$\overline{AB}\cong\overline{PR}$$ means that $$\overline{AB}$$ is congruent to $$\overline{PR}$$.

You can conclude form the above statement that $$AB=PR$$, by the definition of congruent segments.

When you prove triangles congruent by Side-Angle-Side Congruence Theorem, for example, you don't really care what the actual length of both the segments is, but you do care that the figures are congruent.

Therefore, you would say that $$\overline{AB}\cong\overline{PR}$$ instead of $$AB=PR$$

TheXSquaredFactor  Dec 2, 2017

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