+118608 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.
+128406 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
+2440 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?
+118608 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?
+2440 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 \(AB=PR\)
