Question

Given:BD is the altitude of triangle ABC and BD is the median of triangle ABC Prove:triangle ABD is congruent to triangle CBD

Answer 1

Statement

1.

`BD\text{ is the altitude and }the\text{ median of }\Delta ABC`

2.

`AD=DC`

3.

`\angle ADBand\angle CDB\text{ are right triangles}`

4.

`BD=BD`

5.

Reason

1. Given

2. Because BD is the median

3. Because BD is the altitude (def of perpendicular lines)

4. Reflexive property