Question

statement
1 ( \triangle uxy cong \triangle vwy )
2 ( overline{ux} cong overline{vw} )
3 ( overline{uy} cong overline{wy} )
4 ( overline{wy} cong overline{xy} )
5 ( angle uxy cong angle vwy )
6 ( uw = uy + wy )
7 ( vx = vy + xy )
8 ( uw = vy + xy )
9 ( uw = vx )
10 ( \triangle uvx cong \triangle vuw )

reason
1 given
2 cpctc
3 cpctc
4 cpctc
5 cpctc
6
7
8
9
10

Explanation:

Step1: Fill given reason

$\Delta UXY \cong \Delta VWY$ (Given)

Step2: CPCTC for side UX

$\overline{UX} \cong \overline{VW}$ (CPCTC)

Step3: CPCTC for side UY

$\overline{UY} \cong \overline{VY}$ (CPCTC)

Step4: CPCTC for side WY

$\overline{WY} \cong \overline{XY}$ (CPCTC)

Step5: CPCTC for angle UXY

$\angle UXY \cong \angle VWY$ (CPCTC)

Step6: Segment addition postulate (UW)

$UW = UY + WY$ (Segment Addition Postulate)

Step7: Segment addition postulate (VX)

$VX = VY + XY$ (Segment Addition Postulate)

Step8: Substitute congruent segments (UW)

$UW = VY + XY$ (Substitution Property of Equality)

Step9: Transitive property of equality

$UW = VX$ (Transitive Property of Equality)

Step10: SAS congruence

$\Delta UVX \cong \Delta VUW$ (SAS Congruence Rule)

Answer:

Statement	Reason
$\overline{UX} \cong \overline{VW}$	CPCTC
$\overline{UY} \cong \overline{VY}$	CPCTC
$\overline{WY} \cong \overline{XY}$	CPCTC
$\angle UXY \cong \angle VWY$	CPCTC
$UW = UY + WY$	Segment Addition Postulate
$VX = VY + XY$	Segment Addition Postulate
$UW = VY + XY$	Substitution Property of Equality
$UW = VX$	Transitive Property of Equality
$\Delta UVX \cong \Delta VUW$	SAS Congruence Rule