Question

1. in the diagram, \\(\overline{ab} \cong \overline{cd}\\). find the length of \\(\overline{bc}\\). a---(4x - 7)---b---(3x + 4)---c---(2x + 5)---d

Explanation:

Step1: Set AB equal to CD

Since \(\overline{AB} \cong \overline{CD}\), their lengths are equal. So \(4x - 7 = 2x + 5\).

Step2: Solve for x

Subtract \(2x\) from both sides: \(4x - 2x - 7 = 5\), which simplifies to \(2x - 7 = 5\). Then add 7 to both sides: \(2x = 5 + 7 = 12\). Divide both sides by 2: \(x = \frac{12}{2} = 6\).

Step3: Find length of BC

Now substitute \(x = 6\) into the expression for \(BC\), which is \(3x + 4\). So \(3(6) + 4 = 18 + 4 = 22\).

Answer:

22