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Step-by-step explanation:

theres nothing here

Triangle ΔPYX is congruent to triangle ΔYQZ by Angle-Angle-Side condition of congruency

Step-by-step explanation:

The given

Statement                                              Reason

PQR is a triangle                                  Given

XYZR is a parallelogram                      Given

X is the midpoint of RP                        Given

Y  is the midpoint of PQ                        Given

Z  is the midpoint of QR                        Given

Therefore;

QY = YP, Definition of midpoint

XY is parallel to QR, and YZ  is parallel to  RP Midpoint theorem

Therefore, ∠PYX ≅ ∠PQR and ∠QZY ≅ ∠YXP Corresponding angles of parallel lines

From which we have;

Triangle ΔPYX is congruent to triangle ΔYQZ by Angle-Angle-Side condition of congruency.