Question

2. Given the triangle ADC, segment BD is a perpendicular bisector of segment AC Point B is the median of side AC Why would triangle ABD be similar to triangle CBD?

Answer 1

Explanation:

By similar triangles

AB/BC = AD/DC = BD/BD

Hence the two triangles are similar

Answer 2

Explanation:

Consider triangles ABD and CBD

< ABD = < CBD ( both right angles)

AB = CB ( the side AC is bisected by BD)

DB is common to both triangles.

Therefore the triangles are congruent by SAS.

As they are congruent the corresponding angle are equal so they are also similar.