Question

Triangles abd and cbd are shown. triangle a b c is divided into two smaller triangles which are triangle a b d and d b c which share a common side b d. point d lies on segment a c. segment a d is congruent to segment c d. if m∠adb = 110°, what is the relationship between ab and bc?

Answer 1

AB is congruent to BC.

Step-by-step explanation:

Given that triangle ABD and triangle CBD share a common side BD, and AD is congruent to CD, we can conclude that triangle ABD and triangle CBD are congruent by the Side-Angle-Side (SAS) congruence postulate.

Since triangle ABD and triangle CBD are congruent, their corresponding sides are congruent as well. Therefore, AB is congruent to BC.

So, the relationship between AB and BC is that they are congruent (AB ≅ BC).