Question

Complete proofs using angle-side-angle (asa).Given line bd bisect angle abc,bda is congruent to bdc prove abd is congruent to cbd?

Answer 1

To prove that ∠ABD is congruent to ∠CBD using the ASA congruence criterion, we can show that ∠BDA and ∠BDC are congruent and that BD bisects both angles.

Step-by-step explanation:

To prove that ∠ABD is congruent to ∠CBD, we can use the Angle-Side-Angle (ASA) congruence criterion. Given that line BD bisects ∠ABC, we have:

• ∠BDA ≅ ∠BDC (given)
• BD is common to both triangles ABD and CBD (common side)
• ∠ABD and ∠CBD both have line BD bisecting them (angle bisector property)

Based on ASA, we can conclude that triangle ABD is congruent to triangle CBD. This means that the corresponding sides and angles of the two triangles are congruent.

Learn more about ASA congruence