Let's use colors to indicate corresponding vertices in the given congruence.
△ W X Y≅△ W X Z
We will continue to use these colors on the figure.
Considering Congruent Segments
Let's focus on the side with the given length and the corresponding side of the other triangle.
X YandX Z
Since these are corresponding sides in congruent triangles, their measure is the same.
Thhis relationship leads us to setting up and solving an equation for y, by the using the substitution method.
The value that makes segments X Y and X Z congruent is y=4.
Checking Congruent Angles
If triangles â–³ W X Y and â–³ W X Z are congruent, then corresponding angles are also congruent.
Let's check whether this is true for the angles at X in the two triangles when y=4.
This equality shows that for y=4 angles ∠W X Y and ∠W X Z are congruent
Conclusion
For y=4, two sides and the included angle of â–³ W X Y are congruent to the corresponding sides and angle of â–³ W X Z.
Hence, by the Side-Angle-Side (SAS) Congruence Postulate, these two triangles are congruent for y=4.
