Question

activity 1.2 if we know this, then we know that...
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: Identify corresponding vertices

Since $\triangle ABC\cong\triangle DEF$, $A$ corresponds to $D$, $B$ corresponds to $E$, and $C$ corresponds to $F$.

Step2: Determine rigid - motion sequence

First, translate $\triangle ABC$ so that point $A$ coincides with point $D$. Then, rotate $\triangle ABC$ about point $D$ (which is now the same as point $A$) until $\triangle ABC$ coincides with $\triangle DEF$.

Step3: Find the image of segment $BC$

The image of segment $BC$ after the transformation is segment $EF$. Because in congruent triangles $\triangle ABC\cong\triangle DEF$, corresponding sides are congruent and $BC$ corresponds to $EF$.

Step4: Explain side - congruence

We know segments $BC$ and $EF$ are congruent because the definition of congruent triangles states that if $\triangle ABC\cong\triangle DEF$, then all corresponding sides are congruent. $BC$ and $EF$ are corresponding sides of congruent triangles $\triangle ABC$ and $\triangle DEF$.

Step5: Justify angle - congruence

We know that $\angle ABC$ is congruent to $\angle DEF$ because the definition of congruent triangles states that if $\triangle ABC\cong\triangle DEF$, then all corresponding angles are congruent. $\angle ABC$ and $\angle DEF$ are corresponding angles of congruent triangles $\triangle ABC$ and $\triangle DEF$.

Answer:

1. First, translate $\triangle ABC$ so that $A$ coincides with $D$, then rotate $\triangle ABC$ about the new - position of $A$ (which is $D$) until $\triangle ABC$ coincides with $\triangle DEF$.
2. Segment $EF$.
3. In congruent triangles $\triangle ABC\cong\triangle DEF$, corresponding sides are congruent and $BC$ and $EF$ are corresponding sides.
4. In congruent triangles $\triangle ABC\cong\triangle DEF$, corresponding angles are congruent and $\angle ABC$ and $\angle DEF$ are corresponding angles.