Answer:
It seems like you are trying to determine if the two triangles are necessarily congruent and prove it using flowchart proof. This is a common topic in geometry, and some different methods and theorems can help you with this task. One of them is the ASA congruence criterion, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent1.
In your case, you are given that the triangles are ∆AOPR and ∆AEDC and that ∠AOP ≅ ∠AED, ∠APR ≅ ∠ADC, and AP ≅ AD. These are the given statements in your flowchart proof. Based on these statements, you can use the ASA congruence criterion to prove that the triangles are congruent. The final statement is that ∆AOPR ≅ ∆AEDC. You can fill in the flowchart proof as follows:
Type of Statement. Reasonusing
∠AOP ≅ ∠AED | GIVEN
∠APR ≅ ∠ADC | GIVEN
AP ≅ AD GIVEN | GIVEN
∠OAP ≅ ∠EAD | Vertical angles are congruent
∆AOPR ≅ ∆AEDC ASA | congruence criterion
I hope this helps you understand how to determine if the two triangles are necessarily congruent and prove it using a flowchart proof.