Question

if $\triangle abccong\triangle dec$, what is the value of $x$?
a. $x = 8$
b. $x = 5$
c. $x = 4$
d. $x = 1$
e. $x = 2$

Explanation:

Step1: Use congruent triangles property

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

Step2: Set up the equation

Given \(AB = 4x - 1\) and \(DE=x + 2\). Then \(4x-1=x + 2\).

Step3: Solve the equation

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

Answer:

D. \(x = 1\)