Question

5.1 practice - congruent figures
determine if the two figures are congruent. if so, write a congruence statement.

Explanation:

Step1: Check triangle \(ABC\) and \(DEF\)

For \(\triangle ABC\) and \(\triangle DEF\):

• \(\angle A = 35^{\circ}\), \(\angle B=100^{\circ}\), \(\angle C = 45^{\circ}\), \(AB = 10\mathrm{cm}\), \(BC = 8\mathrm{cm}\), \(AC=14\mathrm{cm}\)
• \(\angle D = 100^{\circ}\), \(\angle E = 35^{\circ}\), \(\angle F = 45^{\circ}\), \(DE = 20\mathrm{cm}\), \(EF = 8\mathrm{cm}\), \(DF = 16\mathrm{cm}\)

Since \(AB
eq DE\), \(AC
eq DF\), \(BC = EF\) but other sides and angles - side combinations (by \(ASA\), \(SAS\), \(SSS\) congruence criteria) don't match. So \(\triangle ABC\) and \(\triangle DEF\) are not congruent.

Step2: Check triangle \(ABC\) and \(DEF\) (second pair)

For \(\triangle ABC\) (with \(AC = 10\mathrm{cm}\), \(\angle A=80^{\circ}\), \(AB = 16\mathrm{cm}\), \(\angle B = 40^{\circ}\), \(\angle C=60^{\circ}\), \(BC = 25\mathrm{cm}\)) and \(\triangle DEF\) (with \(DF = 10\mathrm{cm}\), \(\angle D = 80^{\circ}\), \(DE = 16\mathrm{cm}\), \(\angle E=40^{\circ}\), \(\angle F = 60^{\circ}\), \(EF = 25\mathrm{cm}\))
By \(ASA\) (angle - side - angle) congruence criterion:

• \(\angle A=\angle D = 80^{\circ}\)
• \(AC = DF=10\mathrm{cm}\)
• \(\angle C=\angle F = 60^{\circ}\)

Answer:

\(\triangle ABC\cong\triangle DEF\) (by \(ASA\) congruence criterion)