To solve these problems, we need to match the corresponding parts of the congruent triangles. The order of the letters in the congruence statement tells us exactly which vertices, angles, and sides correspond to each other.
1) $\triangle DEF \cong \triangle KJI$
*
Goal: Find what $\overline{FD}$ is congruent to.
*
Step-by-step: Look at the letters in the statement $\triangle DEF \cong \triangle KJI$.
* $D$ corresponds to $K$ (1st letter).
* $E$ corresponds to $J$ (2nd letter).
* $F$ corresponds to $I$ (3rd letter).
* The side $\overline{FD}$ connects the 3rd letter ($F$) and the 1st letter ($D$).
* Therefore, it corresponds to the side connecting the 3rd letter ($I$) and the 1st letter ($K$) in the second triangle.
*
Result: $\overline{IK}$
2) $\triangle BAC \cong \triangle LMN$
*
Goal: Find what $\angle A$ is congruent to.
*
Step-by-step: Look at the position of angle $A$ in the first triangle's name ($\triangle BAC$).
* $A$ is the
2nd letter.
* Now look at the second triangle's name ($\triangle LMN$).
* The
2nd letter is $M$.
* Therefore, angle $A$ corresponds to angle $M$.
*
Result: $\angle M$
3) $\triangle TUV \cong \triangle GFE$
*
Goal: Find what $\angle U$ is congruent to.
*
Step-by-step: Look at the position of angle $U$ in the first triangle's name ($\triangle TUV$).
* $U$ is the
2nd letter.
* Now look at the second triangle's name ($\triangle GFE$).
* The
2nd letter is $F$.
* Therefore, angle $U$ corresponds to angle $F$.
*
Result: $\angle F$
4) $\triangle WVU \cong \triangle GHI$
*
Goal: Find what $\angle W$ is congruent to.
*
Step-by-step: Look at the position of angle $W$ in the first triangle's name ($\triangle WVU$).
* $W$ is the
1st letter.
* Now look at the second triangle's name ($\triangle GHI$).
* The
1st letter is $G$.
* Therefore, angle $W$ corresponds to angle $G$.
*
Result: $\angle G$
Final Answer:
1) $\overline{IK}$
2) $\angle M$
3) $\angle F$
4) $\angle G$
Parent Tip: Review the logic above to help your child master the concept of congruency worksheet.
