Learn Math Questions

from a handpicked tutor in LIVE 1-to-1 classes

from a handpicked tutor in LIVE 1-to-1 classes

# 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:

- All the three corresponding sides of the triangles should be equal.(SSS) or
- Two corresponding sides and a corresponding angle of the triangles should be equal (SAS) or
- Two corresponding angles and one corresponding side of the triangles should be equal (ASA) or
- 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:

- Side AC is common to both the triangles
- Side AD is equal to BC (given)
- 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).

Math worksheets and

visual curriculum

visual curriculum