Question

In quadrilateral ABCD, diagonal BD bisects angle ADC. If AD and CD are equal in length, which equation is true?

1) AB = BC
2) DB = 2DC
3) AB = DB
4) AB = 2AD

Answer 1

In quadrilateral ABCD, if diagonal BD bisects angle ADC and AD and CD are equal in length, then AB = BC.

Step-by-step explanation:

In quadrilateral ABCD, diagonal BD bisects angle ADC. If AD and CD are equal in length, the equation that is true is AB = BC.

Since diagonal BD bisects angle ADC, it divides it into two congruent angles. Also, if AD and CD are equal in length, then triangles ABD and CBD are congruent by Side-Angle-Side (SAS) congruence. Therefore, their corresponding sides AB and BC are also congruent, so the equation AB = BC is true.