Answer:
Given that m∠ABC = m∠CBD, and m∠ABD = m∠ABC + m∠CBD BC bisects m∠ABD (Definition of angle bisector)
Step-by-step explanation:
The given information are;
m∠ABC = m∠CBD
To prove that Ray BC bisects m∠ABD
The description is therefore;
Three lines (AB, BC, and BD) that meet at a point
The content of Box A = m∠ABC = m∠CBD
The content of Box B = m∠ABC ≅ m∠CBD
The content of Box C = Ray BC bisects m∠ABD
Therefore, we have;
m∠ABD = m∠ABC + m∠CBD (Angle addition postulate)
m∠ABC = m∠CBD (Given)
∴ m∠ABC ≅ m∠CBD (Definition of congruent angles)
m∠ABC is adjacent to m∠CBD (Description of the angles)
Line BC is common to m∠ABC and m∠CBD (Description of the angles)
Therefore, given that m∠ABC = m∠CBD, and m∠ABD = m∠ABC + m∠CBD BC bisects m∠ABD (Definition of angle bisector).
