Question

activity: if we know this, then we know that...and are these parts congruent? triangle abc is congruent to triangle def. △abc≅△def 1. find a sequence of rigid motions that takes triangle abc to triangle def. 2. what is the image of segment bc after that transformation? 3. explain how you know those segments are congruent. 4. justify that angle abc is congruent to angle def.

Explanation:

Step1: Translation and rotation

First, translate point A to point D. Then, rotate triangle ABC around point D so that side AB aligns with side DE.

Step2: Image of segment BC

Since $\triangle ABC\cong\triangle DEF$, the corresponding sides are congruent. The image of segment BC after the transformation is segment EF.

Step3: Congruence of segments

By the definition of congruent triangles, if $\triangle ABC\cong\triangle DEF$, then corresponding sides are equal in length. So, $BC = EF$, which means segment BC and segment EF are congruent.

Step4: Congruence of angles

By the definition of congruent triangles, corresponding angles of congruent triangles are congruent. Since $\triangle ABC\cong\triangle DEF$, $\angle ABC$ and $\angle DEF$ are corresponding angles, so $\angle ABC\cong\angle DEF$.

Answer:

1. Translate point A to point D and then rotate around point D to align AB with DE.
2. Segment EF.
3. Corresponding sides of congruent triangles are equal in length.
4. Corresponding angles of congruent triangles are congruent.