Geometry Proof Completion: Reflexive Property

finish this proof with these optioons Given
Reflexive Property
Transitive Property
Addition and Subtraction Properties
Multiplication and Division Properties
Substitution Property
Definition of Congruent Segments
Definition of Midpoint
Definition of Segment Bisector
Definition of Perpendicular
Definition of Perpendicular Bisector
Segment Addition Property
Definition of Congruent Angles
Definition of Right Angle
All right angles are congruent to.
Angle Addition Property
Definition of Angle Bisector
Definition of Supplementary Angles
Definition of Complementary Angles
Vertical Angles Property
Linear Pair Property
If lines ∥, then corr. ∠s congruent to.
If lines ∥, then alt. int. ∠s congruent to.
If lines ∥, then alt. ext. ∠s congruent to.
If lines ∥, then cons. int. ∠s are supp.
Triangle Angle-Sum Property
Exterior Angle Property
SSS Congruence Property
SAS Congruence Property
ASA Congruence Property
AAS Congruence Property
CPCTC Property

Okay, I will complete the proof based on the given information and options.

Задание 10

Statement: $PX = PX$

Reason: Reflexive Property

Explanation:

Steps 8 and 9 state that $WX = YX$, which seems redundant but could be to confuse you. Since $\overline{PX}$ is a perpendicular bisector of $\overline{WY}$, we know that $X$ is the midpoint of $\overline{WY}$, and $\overline{PX}$ is perpendicular to $\overline{WY}$. We want to prove that $WP = YP$.

Since $\overline{PX}$ is perpendicular to $\overline{WY}$, $\angle P X W$ and $\angle P X Y$ are right angles.
All right angles are congruent to each other.
$WX = YX$ by the definition of a perpendicular bisector.
$PX = PX$ by the Reflexive Property.
Therefore, $\triangle P X W \cong \triangle P X Y$ by the SAS Congruence Property.
Finally, $WP = YP$ by CPCTC.

So, the missing step is $PX = PX$ and the reason is the Reflexive Property.

Final Answer:

Statement: $PX = PX$

Reason: Reflexive Property