Question

for # 7 - 10, mark the triangles and complete the congruence statements. 7. △tuv≅△efg 8. △uvw≅△ihg 9. △xyz≅△xcz 10. △def≅△dsr

Explanation:

Step1: Recall congruent - triangle property

In congruent triangles, corresponding angles and corresponding sides are congruent.

Step2: Identify corresponding parts for 7

For $\triangle TUV\cong\triangle EFG$, $T$ corresponds to $E$, $U$ corresponds to $F$, $V$ corresponds to $G$. So $\angle T\cong\angle E$, $\overline{EG}\cong\overline{TV}$, $\angle F\cong\angle U$.

Step3: Identify corresponding parts for 8

For $\triangle UVW\cong\triangle IHG$, $U$ corresponds to $I$, $V$ corresponds to $H$, $W$ corresponds to $G$. So $\angle V\cong\angle H$, $\angle IGH\cong\angle UVW$, $\overline{WV}\cong\overline{HI}$.

Step4: Identify corresponding parts for 9

For $\triangle XYZ\cong\triangle XCZ$, $Y$ corresponds to $C$, $X$ corresponds to $X$, $Z$ corresponds to $Z$. So $\angle YXZ\cong\angle CXZ$, $\overline{YZ}\cong\overline{CZ}$, $\overline{CX}\cong\overline{XY}$.

Step5: Identify corresponding parts for 10

For $\triangle DEF\cong\triangle DSR$, $D$ corresponds to $D$, $E$ corresponds to $S$, $F$ corresponds to $R$. So $\overline{DE}\cong\overline{DS}$, $\angle FDE\cong\angle RDS$, $\overline{DR}\cong\overline{DF}$.

Answer:

1. $\angle T\cong\angle E$, $\overline{EG}\cong\overline{TV}$, $\angle F\cong\angle U$
2. $\angle V\cong\angle H$, $\angle IGH\cong\angle UVW$, $\overline{WV}\cong\overline{HI}$
3. $\angle YXZ\cong\angle CXZ$, $\overline{YZ}\cong\overline{CZ}$, $\overline{CX}\cong\overline{XY}$
4. $\overline{DE}\cong\overline{DS}$, $\angle FDE\cong\angle RDS$, $\overline{DR}\cong\overline{DF}$