Question: Tammy was curious if quadrilaterals $ABCD$ and $FGHE$ were congruent.
She was able to map one figure onto the other using a reflection and a translation.
Tammy concluded:
"I was able to map quadrilateral $ABCD$ onto $FGHE$ using a sequence
of rigid transformations, so the figures are congruent."
What error did Tammy make in her conclusion?
Choose 1 answer:
A Tammy didn't use only rigid transformations, so the
figures are not congruent.
B It's possible to map quadrilateral $ABCD$ onto $FGHE$
using a sequence of rigid transformations, but the
figures are not congruent.
C There is no error. This is a correct conclusion.
1. **State the problem:**
Tammy mapped quadrilateral $ABCD$ onto quadrilateral $FGHE$ using a reflection and a translation and concluded the figures are congruent.
2. **Recall the definition of congruence:**
Two figures are congruent if one can be mapped onto the other using **rigid transformations**.
Rigid transformations include **translations, rotations, and reflections**.
3. **Analyze the transformations used:**
Tammy used a reflection and a translation.
Both are rigid transformations.
4. **Conclusion:**
Since $ABCD$ can be mapped onto $FGHE$ by a sequence of rigid transformations, the two quadrilaterals are congruent.
5. **Check the answer choices:**
- A is incorrect because Tammy did use only rigid transformations.
- B is incorrect because if figures can be mapped by rigid transformations, they are congruent.
- C is correct because Tammy's conclusion is valid.
**Final answer:**
Tammy made no error; her conclusion is correct.
**Answer: C**