The complete two-column proof that shows that ∠DBC ≅ ∠DCB using the definition of isosceles triangle is given in the image attached below.
What is an Isosceles Triangle?
Two sides directly opposite the two base angles of an isosceles triangle are congruent, so also are the two base angles congruent.
From the given diagram, we are told that:
AB ≅ AC and ∠BAD ≅ ∠CAD
Also, AD ≅ DA based on the reflexive property.
Thus, it implies that,
ΔBAD ≅ ΔCAD based on the SAS congruence theorem, because they have two pairs of congruent sides and one pair of congruent included angles.
Thus, since both triangles are congruent, therefore, DB = DC by CPCTC theorem.
Therefore, by the definition of isosceles triangle, ∠DBC ≅ ∠DCB.
Thus, the complete two-column proof that shows that ∠DBC ≅ ∠DCB using the definition of isosceles triangle is given in the image attached below.
Learn more about isosceles triangle on:
https://brainly.com/question/11884412
