Question
Examine the diagram shown.
Which of the following will prove that ΔABD ≅ΔCBD
?
A.AAS
B.SAS
C.SSA
D.ASA
Which of the following will prove that ΔABD ≅ΔCBD
?
A.AAS
B.SAS
C.SSA
D.ASA
Answers
GPT-4o mini
To determine which congruence criteria can prove that triangles ΔABD and ΔCBD are congruent, we need to analyze the structure of the triangles.
Given that:
- A and C are points on line segment BD.
- Points A and C are distinct, meaning they are not the same point.
- Common side BD would be part of both triangles.
- Angles at either point A or point C could confirm congruence based on given angle information.
Based on the context of congruency criteria:
- AAS (Angle-Angle-Side): Needs two angles and a non-included side.
- SAS (Side-Angle-Side): Needs two sides and the included angle.
- SSA (Side-Side-Angle): Two sides and a non-included angle; however, this does not guarantee congruency due to the "ambiguous case."
- ASA (Angle-Side-Angle): Needs two angles and the included side.
Since both triangles share the side BD (this can act as one congruent side), if we can establish one angle from each triangle (let's say ∠ABD and ∠CBD), we can then determine congruency using either AAS or ASA. However, ASA clearly fits as it requires two angles and the included side, which would be BD.
Therefore, the most appropriate option to confirm that ΔABD ≅ ΔCBD is:
**D. ASA**
Given that:
- A and C are points on line segment BD.
- Points A and C are distinct, meaning they are not the same point.
- Common side BD would be part of both triangles.
- Angles at either point A or point C could confirm congruence based on given angle information.
Based on the context of congruency criteria:
- AAS (Angle-Angle-Side): Needs two angles and a non-included side.
- SAS (Side-Angle-Side): Needs two sides and the included angle.
- SSA (Side-Side-Angle): Two sides and a non-included angle; however, this does not guarantee congruency due to the "ambiguous case."
- ASA (Angle-Side-Angle): Needs two angles and the included side.
Since both triangles share the side BD (this can act as one congruent side), if we can establish one angle from each triangle (let's say ∠ABD and ∠CBD), we can then determine congruency using either AAS or ASA. However, ASA clearly fits as it requires two angles and the included side, which would be BD.
Therefore, the most appropriate option to confirm that ΔABD ≅ ΔCBD is:
**D. ASA**