Question

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∠BDC = 70°, what is the relationship between AB and BC?

AB = BC
AB < BC
AB > BC
AB + BC < AC

Answer 1

Given that segment AD is congruent to segment CD and m°BDC = 70°, triangles ABD and BCD are congruent, which means AB is congruent to BC.

Step-by-step explanation:

If m∠BDC = 70° and segment AD is congruent to segment CD, then triangle ADC is an isosceles triangle with base angles ADC and DAC being congruent. Therefore, if ΔBDC has one angle that is 70°, then angle ABC must also be 70° (since AD is congruent to CD, it implies that angle ABC is congruent to angle ADC). Since triangle ABD shares angle B with triangle BCD, and we know the base angles at D are the same, triangle ABD must also be congruent to triangle BCD. Consequently, this implies that AB is congruent to BC. Therefore, the correct relationship is AB = BC.