Question

in the diagram, ( abgh = cdef ).

1. identify all pairs of congruent corresponding parts.
2. find the value of ( x ).

Explanation:

Step1: Identify congruent corresponding parts

Since \(ABGH\cong CDEF\), the corresponding parts are congruent.

• Angles: \(\angle A\cong\angle C\), \(\angle B\cong\angle D\), \(\angle H\cong\angle F\), \(\angle G\cong\angle E\)
• Sides: \(AB\cong CD\), \(BG\cong DE\), \(GH\cong EF\), \(HA\cong FC\)

Step2: Use angle - congruence to find \(x\)

We know that \(\angle H\cong\angle F\). So \(6x + 5=105\)
Subtract \(5\) from both sides: \(6x=105 - 5\)
\(6x = 100\)
Divide both sides by \(6\): \(x=\frac{100}{6}=\frac{50}{3}\approx16.67\)

Answer:

1. Congruent corresponding angles: \(\angle A\cong\angle C\), \(\angle B\cong\angle D\), \(\angle H\cong\angle F\), \(\angle G\cong\angle E\); Congruent corresponding sides: \(AB\cong CD\), \(BG\cong DE\), \(GH\cong EF\), \(HA\cong FC\)
2. \(x = \frac{50}{3}\)