Here, we have two congruent triangles.
Given:
ST = 3x - 1 XY = 4x - 5
SW = 3x + 1 XZ = 4x - 3
TW = 2x + 1 YZ = x + 5
Since triangle STW and triangle XYZ are congruent, they have exactly the same corresponding sides.
To find the value of x, equate the corresponding sides and evaluate.
ST = XY
SW = XZ
TW = YZ
Take one of the corresponding sides.
We have:
ST = XY
3x - 1 = 4x - 5
Subtract 4x from both sides:
3x - 4x - 1 = 4x - 4x - 5
-x - 1 = -5
Add 1 to both sides:
-x - 1 + 1 = -5 + 1
-x = -4
Divide both sides by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{-4}{-1} \\ \\ x=4 \end{gathered}[/tex]
Therefore, the value of x that makes ΔSTW ≅ ΔXYZ is 4
ANSWER:
x = 4
