Answer:
We are given that,
Polygons ABC and DBC are triangles.
Also, ABC and DBC are Right Triangles as ∠ABC and ∠DBC are 90 respectively.
AB ↔ CD
Now,
From the HL Congruency we know that,
"Two Right triangles are congruent if the Hypotenuses and at least One Side of both the triangles correspond to each other."
Here,
- Triangles ABC and DBC were given to be right triangles.
- AB and CD are the hypotenuses of ΔABC and Δ DBC respectively. (From the construction of the figure) and are given equal.
- The Side BC of both the triangles correspond as they share the side BC together.
Here, As the three conditions of being congruent through HL Congruency are satisfied, ΔABC & Δ DBC are congruent through the HL Congruency Criterion.
ΔABC ≅ Δ DBC [Hence, Proved]
