Question

δuvw ≅ δtiw. complete the proof that δtuv ≅ δutw.
1 δuvw ≅ δtiw
2 overline{tw} ≅ overline{uv}
3 overline{tv} ≅ overline{uw}
4 overline{tu} ≅ overline{tu}
5 δtuv ≅ δutw

Explanation:

Step1: Given

$\triangle UVW\cong\triangle TIW$ is given.

Step2: Corresponding parts of congruent triangles

Since $\triangle UVW\cong\triangle TIW$, by the property of congruent triangles (corresponding parts of congruent triangles are congruent), we have $\overline{TI}\cong\overline{UV}$.

Step3: Corresponding parts of congruent triangles

Also, $\overline{TV}\cong\overline{UW}$ (corresponding parts of congruent triangles are congruent).

Step4: Reflexive property

For any segment $\overline{AB}$, $\overline{AB}\cong\overline{AB}$. So, $\overline{TU}\cong\overline{TU}$ (reflexive property of congruence).

Step5: SSS (Side - Side - Side) congruence criterion

In $\triangle TUV$ and $\triangle UTW$, we have $\overline{TI}\cong\overline{UV}$, $\overline{TV}\cong\overline{UW}$, and $\overline{TU}\cong\overline{TU}$. By the SSS (Side - Side - Side) congruence criterion, $\triangle TUV\cong\triangle UTW$.

Answer:

1. Given
2. Corresponding parts of congruent triangles
3. Corresponding parts of congruent triangles
4. Reflexive property of congruence
5. SSS (Side - Side - Side) congruence criterion