Question

Use the image to answer the question. If you wanted to explain why △ABD≅CBD by the SAS Congruence Theorem, which of the following would be helpful to know? (1 point) Responses AC¯¯¯¯¯¯¯¯ is the angle bisector of ∠BAD. Modifying above upper A upper C with bar is the angle bisector of angle upper B upper A upper D . AC¯¯¯¯¯¯¯¯ is the angle bisector of ∠BCD. Modifying above upper A upper C with bar is the angle bisector of angle upper B upper C upper D . BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠ABC. Modifying above upper B upper D with bar is the angle bisector of angle upper A upper B upper C . BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠BCD.

Answer 1

To show that triangles △ABD and △CBD are congruent by the SAS (Side-Angle-Side) Congruence Theorem, we need to establish that there are two pairs of sides that are equal and the included angle between them is also equal.

1. Side Information: You need to know the lengths of sides AB and CB, and whether they are equal. This is typically shown by the angle bisector property or construction.

2. Angle Condition: Also, knowing that AC is the angle bisector of ∠BAD would be helpful because it would imply that ∠CAB is equal to ∠DAC. This gives you the necessary angle information to apply the SAS theorem.

Based on the options given, the most relevant information would be:

• AC is the angle bisector of ∠BAD.

This gives you that ∠CAB ≅ ∠DAC and if you also know that AB = CB (which might be part of different considerations or figures), you could then show the triangles are congruent by the SAS theorem.