Question

What additional information do you need to prove the two triangles congruent by ASA?(1 point)Responses∠E≅∠O∠𝐸≅∠𝑂∠E≅∠O∠𝐸≅∠𝑂PE¯¯¯¯¯¯¯¯≅DO¯¯¯¯¯¯¯¯𝑃𝐸¯≅𝐷𝑂¯line segment cap p cap e is congruent to line segment cap d cap oET¯¯¯¯¯¯¯≅OG¯¯¯¯¯¯¯¯𝐸𝑇¯≅𝑂𝐺¯line segment cap e cap t is congruent to line segment cap o cap gPT¯¯¯¯¯¯¯≅DG¯¯¯¯¯¯¯¯

Answer 1

To prove two triangles congruent using the Angle-Side-Angle (ASA) postulate, you need two angles and the included side of one triangle to be congruent to two angles and the included side of the other triangle respectively.

From your description, you have:

1. \( \angle E \cong \angle O \)
2. \( \overline{PE} \cong \overline{DO} \) (the side between the angles)
3. \( \overline{ET} \cong \overline{OG} \)

To ensure the two triangles are proved congruent by ASA, you need:

- The second angle from the first triangle should be compared with the second triangle.

Thus, you would need the following additional information:

- **Another angle congruence**: You need an angle in the first triangle that is congruent to a corresponding angle in the second triangle (for example \( \angle T \cong \angle G \)).

With this information, you would have two angles and the included side for both triangles, allowing you to conclude that the triangles are congruent by the ASA postulate.