Question

Which of the following criterion will accurately complete the proof in step 4

Answer 1

2.

`\begin{gathered} \angle RAG\text{ and }\angle RET\text{ are vertical angles} \\ \Rightarrow\angle RAG\cong\angle RET \end{gathered}`

The reason for 2 is 'the angles are vertical'.

3. In the diagram below, we can identify the alternate interior angles more easily

Therefore, Therefore, the statements of the third step are

`\begin{gathered} \angle AGR\cong\angle ETR \\ \text{and} \\ \angle GAR\cong\angle\text{TER} \end{gathered}`

Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.