Based on the given information in the figure at the right, how can you justify that triangle ABC is congruent to triangle CDA?ASA, SSS, AAS, SAS

Solution:

To establish congruence of any two triangles certain conditions need to be fulfilled. For two triangles to be congruent:

1. All the three corresponding sides of the triangles should be equal.(SSS) or
2. Two corresponding sides and a corresponding angle of the triangles should be equal (SAS) or
3. Two corresponding angles and one corresponding side of the triangles should be equal (ASA) or
4. The right angle-hypotenuse-side congruence (RHS)

In the diagram above the congruence in the triangles, △ABC and △CDA need to be investigated. As per the diagram:

1. Side AC is common to both the triangles
2. Side AD is equal to BC (given)
3. Angle ∠DAC is equal to ∠ACD (alternate angles as depicted in the diagram)

Hence the condition two sides and an included angle(SAS) of both the triangles are equal and hence △ABC and △CDA are congruent.

Based on the given information in the figure at the right, how can you justify that triangle ABC is congruent to triangle CDA?

Summary:

Triangle ABC is congruent to triangle CDA and it is established by the fulfillment of the condition SAS (two sides and an included angle).