Question

which side in △xgr corresponds with side rz?
which side in △rpz corresponds with side gr?
what is the scale factor applied to △rpz to achieve △rgx? scale factor = (fraction)

Explanation:

Step1: Identify corresponding sides

In intersecting triangles, opposite angles at R are equal. Corresponding sides are proportional. For △XGR and △ZPR (△RPZ), side RZ in △RPZ corresponds to RX in △XGR (shared vertex R, opposite angles). Side GR in △XGR corresponds to RZ in △RPZ? No, check labels: △XGR has sides XG, GR, RX; △RPZ has sides RP, PZ, ZR. Corresponding sides: RX ↔ RZ, GR ↔ RP, XG ↔ ZP.

Step2: Calculate scale factor

Scale factor = (side of △RGX) / (side of △RPZ). Use RX=19, RZ=76: scale factor = 19/76 = 1/4.

Answer:

RX
RP
$\frac{1}{4}$