Question

Consider isosceles triangle abc with angle bisector ad¯¯¯¯¯¯¯¯. Triangle abc. Side ab and side ac each have a single slash mark. Point d lies on side bc, creating line segment ad. What reasons complete the proof of ∠b≅∠c? Drag the phrases to the empty boxes to complete the proof correctly.

Answer 1

To prove that ∠b is congruent to ∠c, we can use the Angle Bisector Theorem. According to the theorem, if a line segment (AD) bisects an angle in a triangle and the line segment is an angle bisector, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Step-by-step explanation:

To prove that ∠b is congruent to ∠c, we can use the Angle Bisector Theorem. According to the theorem, if a line segment (AD) bisects an angle in a triangle and the line segment is an angle bisector, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. In this case, since triangle ABC is isosceles, we know that side AB is congruent to side AC. Therefore, if the angle bisector AD divides side BC into two segments BD and CD, then segments BD and CD are congruent.