Question
Use the image to answer the question.
Two triangles have a common adjacent side and congruent angles.
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
CE¯¯¯¯¯¯¯¯≅CQ¯¯¯¯¯¯¯¯
Modifying above upper C upper E with bar congruent to Modifying above upper C upper Q with bar
∠DCE≅∠DCQ
angle upper D upper C upper E congruent to angle upper D upper C upper Q
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Two triangles have a common adjacent side and congruent angles.
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
CE¯¯¯¯¯¯¯¯≅CQ¯¯¯¯¯¯¯¯
Modifying above upper C upper E with bar congruent to Modifying above upper C upper Q with bar
∠DCE≅∠DCQ
angle upper D upper C upper E congruent to angle upper D upper C upper Q
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Answers
GPT-4o mini
To prove triangles CDE and CDQ congruent by ASA (Angle-Side-Angle), you need to ensure that you have two angles and the included side that are congruent. Given that the triangles already have a common adjacent side (CD) and congruent angles (let's refer to them as ∠CDE and ∠CDQ), you need to establish the congruence of one additional angle or side.
Among the options provided, the additional information needed is:
**∠E≅∠Q**
This means that angle E must be congruent to angle Q. With this information, you will have two angles (∠CDE and ∠E≅∠Q) and the included side (CD), which are sufficient to prove the triangles CDE and CDQ congruent by ASA.
Among the options provided, the additional information needed is:
**∠E≅∠Q**
This means that angle E must be congruent to angle Q. With this information, you will have two angles (∠CDE and ∠E≅∠Q) and the included side (CD), which are sufficient to prove the triangles CDE and CDQ congruent by ASA.