Question

1. ( \triangle cpncong\triangle biy ). identify all pairs of congruent corresponding angles and corresponding sides.

in the diagram below, ( \triangle efgcong\triangle opq ), complete #2 - 7.

1. ( overline{ef}cong )____
2. ( angle pcong )____
3. ( angle gcong )____
4. ( mangle o= )____
5. ( qo= )____
6. ( \triangle gfecong )____

Explanation:

Step1: Use congruent triangle properties

Since \(\triangle EFG\cong\triangle OPQ\), corresponding parts are congruent.
For side \(\overline{EF}\), its corresponding side in \(\triangle OPQ\) is \(\overline{OP}\) (by order of congruence \(E - O\), \(F - P\), \(G - Q\)). So \(\overline{EF}\cong\overline{OP}\).

Step2: For \(\angle P\)

\(\angle P\) corresponds to \(\angle F\) (from \(\triangle EFG\cong\triangle OPQ\)). So \(\angle P\cong\angle F\).

Step3: For \(\angle G\)

\(\angle G\) corresponds to \(\angle Q\). So \(\angle G\cong\angle Q\).

Step4: For \(m\angle O\)

\(\angle O\) corresponds to \(\angle E\). Given \(m\angle E = 110^{\circ}\), so \(m\angle O=110^{\circ}\).

Step5: For \(QO\)

\(QO\) corresponds to \(GE\). Given \(GE = 7\mathrm{km}\), so \(QO = 7\mathrm{km}\).

Step6: For \(\triangle GFE\)

\(\triangle GFE\) (which is same as \(\triangle EFG\)) corresponds to \(\triangle QOP\) (same as \(\triangle OPQ\)). So \(\triangle GFE\cong\triangle QOP\).

Answer:

1. \(\overline{OP}\)
2. \(\angle F\)
3. \(\angle Q\)
4. \(110^{\circ}\)
5. \(7\mathrm{km}\)
6. \(\triangle QOP\)