What additional information is needed in order to prove triangles CDE and CDQ congruent by ASA? (1 point) Responses ∠E≅∠Q angle upper E congruent to angle upper Q DE¯¯¯¯¯¯¯¯≅DQ¯¯¯¯¯¯¯¯ Modifying above upper D upper E with bar congruent to Modifying above upper D upper Q with bar ∠DCE≅∠DCQ angle upper D upper C upper E congruent to angle upper D upper C upper Q CE¯¯¯¯¯¯¯¯≅CQ¯¯¯¯¯¯¯¯

Question

the image:

The image shows two triangles, ( \triangle CDE ) and ( \triangle CDQ ), sharing a common side ( \overline{CD} ). Here are the details:

Vertices:
( C ) is the top vertex of both triangles.
( D ) is the bottom right vertex of both triangles.
( E ) is the bottom left vertex of ( \triangle CDE ).
( Q ) is the bottom left vertex of ( \triangle CDQ ).
Sides:
( \overline{CD} ) is the shared side between the two triangles.
( \overline{CE} ) and ( \overline{CQ} ) are the other sides of ( \triangle CDE ) and ( \triangle CDQ ), respectively.
Angles:
( \angle DCE ) and ( \angle DCQ ) are the angles at vertex ( C ) for ( \triangle CDE ) and ( \triangle CDQ ), respectively.
( \angle E ) and ( \angle Q ) are the angles at vertices ( E ) and ( Q ), respectively.
To prove ( \triangle CDE \cong \triangle CDQ ) by ASA, you need to show:

( \angle E \cong \angle Q )
( \angle DCE \cong \angle DCQ )
( \overline{DE} \cong \overline{DQ} )

Answer 1

To prove the triangles \( \triangle CDE \) and \( \triangle CDQ \) congruent by the Angle-Side-Angle (ASA) criterion, you need to establish two angles and the included side between them as congruent.

Based on your description, here is what you would need:

1. Angle Congruence: You need to show that \( \angle E \cong \angle Q \) (the angles at vertices E and Q, respectively). This will contribute to one of the angle pairs needed for ASA.

2. Angle Congruence: You need to affirm that \( \angle DCE \cong \angle DCQ \) (the angles at vertex C in both triangles). This is the second angle pair that is required.

3. Side Congruence: Lastly, you need to demonstrate that the side \( \overline{DE} \cong \overline{DQ} \) (the sides opposite the two angles that were established as congruent). This side is the included side between the two pairs of angles.

In summary, to prove \( \triangle CDE \cong \triangle CDQ \) using ASA, you need to validate the following:

• \( \angle E \cong \angle Q \)
• \( \angle DCE \cong \angle DCQ \)
• \( \overline{DE} \cong \overline{DQ} \)

If these conditions are met, you can conclude that the triangles are congruent by ASA.