Question

select the correct answer.
if \\( \triangle a b c \cong \triangle d e c \\), what is the value of \\( x \\)?
a. \\( x = 8 \\)
b. \\( x = 5 \\)
c. \\( x = 4 \\)
d. \\( x = 1 \\)
e. \\( x = 2 \\)

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEC\), their corresponding sides are equal. So, \(AB = DE\).

Step2: Set up the equation

We know that \(AB=4x - 1\) and \(DE=x + 2\). Then the equation is \(4x-1=x + 2\).

Step3: Solve the equation

Subtract \(x\) from both sides: \(4x-x-1=x-x + 2\), which simplifies to \(3x-1=2\).
Add \(1\) to both sides: \(3x-1 + 1=2+1\), so \(3x=3\).
Divide both sides by \(3\): \(\frac{3x}{3}=\frac{3}{3}\), then \(x = 1\).

Answer:

D. \(x = 1\)