Question

In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of " title=" \angle" alt=" \angle" align="absmiddle" class="latex-formula"> XYZ and $\angle$ XZY respectively. Prove that YQ = ZP.
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Answer 1

Answer:

this is your answer. look at this once.

Answer 2

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

$1)\, XY=XZ$                                              Given

$2) m\angle Y= m\angle Z$                                        Isosceles Triangle Theorem

$\displaystyle 3) m\angle Y=m\angle XYQ + \angle QYZ$                  Angle Addition

$\displaystyle 4)\text{ YQ bisects \angle XYZ }$                               Given

$5) m\angle XYQ=m\angle QYZ$                           Definition of Bisector

$\displaystyle 6)m\angle Y=2m\angle QYZ$                               Substitution

$7)m\angle Z=m\angle XZP+m\angle PZY$              Angle Addition

$8)\text{ ZP bisects \angle XZY }$                              Given

$\displaystyle 9) m\angle XZP=m\angle PZY$                          Definition of Bisector

$\displaystyle 10) m\angle Z = 2m\angle PZY$                            Substitution

$11)\text{ } 2m\angle QYZ=2m\angle PZY$                    Substitution

$12)\text{ }m\angle QYZ=m\angle PZY$                        Division Property of Equality

$13)\text{ } YZ=YZ$                                         Reflexive Property

$14)\text{ } \Delta YZP\cong\Delta ZYQ$                             Angle-Side-Angle Congruence*

$15)\text{ } YQ=ZP$                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ