Question

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

Explanation:

Step1: Check corresponding sides and angles

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

• \(AB = DE=16\mathrm{cm}\)
• \(AC = DF = 10\mathrm{cm}\)
• \(BC=EF = 25\mathrm{cm}\)
• \(\angle A=\angle D = 80^{\circ}\)
• \(\angle B=\angle E=40^{\circ}\)
• \(\angle C=\angle F = 60^{\circ}\)

Step2: Write congruence statement

Since all corresponding sides and angles are equal, by the Side - Angle - Side (SAS), Angle - Side - Angle (ASA), or Side - Side - Side (SSS) congruence criteria (in this case SSS as all three sides are equal and angles are equal due to side - side - side equality in a triangle implies angle equality), the two triangles are congruent.

Answer:

\(\triangle ABC\cong\triangle DEF\)