Multiple Choice
Based on the given information in the figure at the right, how can you justify that triangleABC congruent to triangleCDA?
Quadrilateral A B C D is shown. Segment A C divides the figure into 2 triangles. Sides B C and A D are marked with single congruence marks. Segment A C is marked with a double congruence mark. Angles A C B and C A D are each marked with a single congruence arc.
(1 point)
Responses
ASA
ASA
SSS
SSS
AAS
AAS
SAS
SAS
Based on the given information, the triangles can be justified as congruent using the SAS (Side-Angle-Side) criteria.
To justify that triangle ABC is congruent to triangle CDA, we can use the SAS (Side-Angle-Side) congruence criterion.
According to the given information, we know that side BC is congruent to side AD, as indicated by the single congruence marks. Additionally, we know that segment AC is marked with a double congruence mark, which means it is congruent to itself. Finally, we can see that angles ACB and CAD are marked with single congruence arcs, indicating that they are congruent.
By using the SAS congruence criterion, we have the following congruent parts:
- Side BC ≅ Side AD
- Angle ACB ≅ Angle CAD
- Segment AC ≅ Segment AC
Therefore, we have enough information to justify that triangle ABC is congruent to triangle CDA using the SAS congruence criterion.