In triangle PLY, where A is the midpoint of PY, statements 1-5 are true. LY = PY, LP = YP by midpoint definition. PL = LY due to the reflexive property.
PL ≅ YP by SSS congruence.
The statements in the table. The statements are all about the properties of triangle PLY, given that PLYL and point A is the midpoint of PY.
Based on the given information, we can say that:
* Statement 1 (LY = PY) is true by the definition of a midpoint. A midpoint divides a segment into two segments with equal lengths.
* Statement 2 (LP = YP) is also true for the same reason.
* Statement 3 (PL = LY) is true because of the reflexive property of congruence. Every segment is congruent to itself.
* Statement 4 (PL = YP) follows from statements 1 and 3. We know that LY = PY and PL = LY, so PL must also be equal to YP.
* Statement 5 (PL congruent to YP) can be proven using SSS congruence. We have established that PL = LY = YP, so all three sides of triangle PLY are congruent to the corresponding sides of triangle YPL.
Therefore, the answer is yes for all the statements in the table.