Question

select the correct answer

if ( \triangle abccong\triangle dec ), what is the value of ( x )?

( \bigcirc a quad x = 8 )
( \bigcirc b quad x = 5 )
( \bigcirc c quad x = 4 )
( \bigcirc d quad x = 1 )
( \bigcirc e quad 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 \(3\): \(x=\frac{3}{3}=1\).

Answer:

D. \(x = 1\)