Question

1. here are two figures. use the given information to fill in the sentence frames that describe the rigid motions that would prove that triangle edf is congruent to triangle abc.

• we will first ____ figure def by the directed line segment __. now point __ is on point ____.
• we will then ____ figure def on center d by angle __. since segment df is congruent to segment ac, point __ will land on point __. and since segment de is congruent to ab, then point ____

Explanation:

Step1: Translate the figure

Translate figure \(DEF\) by the directed line segment \(DA\). Now point \(D\) is on point \(A\).

Step2: Rotate the figure

Rotate figure \(D'E'F'\) on center \(D'\) (which is now \(A\)) by angle \(\angle DAB\). Since segment \(DF\) is congruent to segment \(AC\), point \(F\) will land on point \(C\). And since segment \(DE\) is congruent to \(AB\), then point \(E\) will land on point \(B\).

Answer:

We will first \(\text{translate}\) figure \(DEF\) by the directed line segment \(\text{DA}\). Now point \(\text{D}\) is on point \(\text{A}\). We will then \(\text{rotate}\) figure \(D'E'F'\) on center \(D'\) by angle \(\angle DAB\). Since segment \(DF\) is congruent to segment \(AC\), point \(\text{F}\) will land on point \(\text{C}\). And since segment \(DE\) is congruent to \(AB\), then point \(\text{E}\) will land on point \(\text{B}\).