In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of XYZ and XZY respectively. Prove that YQ = ZP. ~Thanks in advance ! ♡

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

                                             Given

                                       Isosceles Triangle Theorem

                 Angle Addition

                              Given

                          Definition of Bisector

                              Substitution

             Angle Addition

                             Given

                         Definition of Bisector

                           Substitution

                   Substitution

                       Division Property of Equality

                                        Reflexive Property

                            Angle-Side-Angle Congruence*

                                        CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

this is your answer. look at this once.