1. Triangle $LMN$ is translated to create triangle $L'M'N'$. If the length of side $\overline{LM}$ is 12 cm, what is the length of side $\overline{L'M'}$ in cm? The answer is ___.
2. A figure undergoes a translation. Which statement about the resulting image is always true?
3. Pentagon $ABCDE$ is translated, resulting in pentagon $A'B'C'D'E'$. If the measure of $\angle BCD$ is $108^\circ$, what is the measure of $\angle B'C'D'$ in degrees? The answer is ___.
4. A line segment $\overline{PQ}$ with a length of 15 units is transformed. Its image, $\overline{P'Q'}$, has a length of 10 units. Can this transformation be a translation?
5. A rectangle with a perimeter of 30 meters is translated. What is the perimeter of the translated rectangle in meters? The answer is ___.
6. Triangle $ABC$ has sides of length 5, 7, and 8. Triangle $XYZ$ has corresponding sides of length 5, 7, and $k$. For the triangles to be non-congruent ($ riangle ABC \not\cong riangle XYZ$), the value of $k$ cannot be ___.
7. A rectangle has four $90^\circ$ angles. A parallelogram has angles of $80^\circ$ and $100^\circ$. Even if their side lengths are identical, why are these two figures not congruent?
8. In $\triangle LMN$, side $LM = 20$ cm. In $\triangle PQR$, the corresponding side $PQ = 21$ cm. Because the corresponding sides $LM$ and $PQ$ are unequal, we can conclude that $\triangle LMN \not\cong \triangle PQR$. This is true because $20 \neq$ ___.
9. To prove that two polygons are not congruent, what is the minimum information you need to find?
10. Consider $\triangle GHI$ with $\angle G = 40^\circ$ and $\triangle JKL$ with corresponding $\angle J = 50^\circ$. What can be concluded about the two triangles?