Question 822137
Extend the segments so that there are multiple angles at A , B and C .
Assign numbers to angles, beginning with angle ABZ. Call
angle ABZ, angle 1.  Around B, label the angles clockwise as angles
2, 3 and 4.
Around A, begin with angle ZAB, label it as 5.  Label clockwise 6 , 7 and 8.
Around P, begin with angle ZPQ, label it as 9.  Label clockwise 10, 11 and 12.
Around Q, begin with angle ZQP, label it as 13. Label clockwise 14, 15 and 16.

Angle 4 = angle 14, corresponding angles of diagonal intersecting || lines.
Angle 1 = angle 13, supplementary angles.
Angle 8 = angle 10, corresponding angles of diagonal intersecting || lines.
Angle 9 = angle 5, supplementary angles.
So ABZ is congruent with QPZ , by angle/side/angle.
BZ congruent with ZQ since these sides are opposite angels 5 and 9 of congruent
triangles.

I hope this helps.