Question

1. △abc≅△def. ab = 2x - 10, and de = x + 20. find the value of x and ab.

Explanation:

Step1: Use the property of congruent triangles

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

Step2: Solve the equation for \(x\)

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

Step3: Find the value of \(AB\)

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

Answer:

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