Question

is \\( \triangle a b c \\) congruent to \\( \triangle d e f \\) ? justify your answer using rigid motions

Explanation:

Step1: Check for congruence using SAS (Side - Angle - Side)

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

• \(AC = DF\) (marked with one tick)
• \(\angle C=\angle F = 80^{\circ}\)
• \(BC = EF\) (marked with two ticks)

By the SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle DFE\)

Step2: Check for rigid motion (rotation)

A rotation can map \(\triangle ABC\) onto \(\triangle DEF\). Rotation is a rigid motion that preserves the shape and size of the figure. If we rotate \(\triangle ABC\) around a suitable center (the intersection point of the perpendicular bisectors of the segments joining corresponding vertices), we can align \(A\) with \(D\), \(B\) with \(E\), and \(C\) with \(F\)

Answer:

Yes. A rotation can map \(\triangle ABC\) onto \(\triangle DEF\)