Question

part d
write and solve an equation for each of the following.

1. \\( \triangle a b c \cong \triangle d e f \\). \\( a b = 2 x - 10 \\) and \\( d e = x + 20 \\). find the values of \\( x \\) and \\( a b \\).

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), then \(AB = DE\). So, we set up the equation \(2x-10=x + 20\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(2x-x-10=x-x + 20\), which simplifies to \(x-10=20\).
Add \(10\) to both sides: \(x-10 + 10=20+10\), so \(x = 30\).

Step3: Find the value of \(AB\)

Substitute \(x = 30\) into \(AB=2x-10\). Then \(AB=2\times30-10\).
First, calculate \(2\times30 = 60\). Then \(60-10=50\).

Answer:

\(x = 30\) and \(AB = 50\)