Question

use the diagram to complete the statements. segment ad must be congruent to segment segment bc must be congruent to segment

Explanation:

Step1: Analyze triangle congruence

Since the line is a perpendicular bisector (right - angle and equal segments on the bisected line), we can use the Hypotenuse - Leg (HL) congruence criterion for right - triangles.
For right - triangles \( \triangle ABD\) and \( \triangle ABE\), \(AB = AB\) (common side), and the segments on the perpendicular bisector are equal. So, \( \triangle ABD\cong\triangle ABE\) by HL. Then \(AD = AE\) (corresponding parts of congruent triangles).

Step2: Analyze another pair of triangles

For right - triangles \( \triangle CBD\) and \( \triangle CBE\), \(CB = CB\) (common side), and the segments on the perpendicular bisector are equal. So, \( \triangle CBD\cong\triangle CBE\) by HL. Then \(BC = BD\) (corresponding parts of congruent triangles).

Answer:

Segment AD must be congruent to segment AE.
Segment BC must be congruent to segment BD.