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The triangles RST and XYZ are congruent. Points P and W lie on ST and YZ, respectively. Which of the following statements are true?

A) if P is the midpoint of line ST and W is the midpoint of line YZ, then $\triangle RSP\cong \triangle XYW.$

B) If line RP bisects angle SRT and line XW bisects angle YXZ, then $\triangle RSP\cong \triangle XYW$

C) If RP = XW, then $\triangle RSP\cong \triangle XYW$

D) If $\overline {RP}\perp\overline {ST} and \overline {XW}\perp\overline{YZ}, then \triangle RSP\cong \triangle XYW$