Question

Given triangle ABC, where ray of BD is an altitude and AD=CD. Prove triangle ADB is congruent to triangle CDB. Write in statement and proof form....

Answer 1

The altitude is always perpendicular to the base so angle ADB is the same as CDB. Sides AD = DC (given), and DB = DB (reflexive) so ADB is congruent to CDB by side-angle-side.

Answer 2

(1)ABD=CBD --> bisected by BD
(2)BD=BD --> reflexive property
(3)AD=CD --> given

Answer 3

1. Segment BD is an altitude of Triangle ABC, drawn to Segment AC  Given
2. Segment BD is perpendicular to Segment AC  Definition of Altitude
3. AD = DC  Given
4. Segment BD is the perpendicular-bisector of Segment AC  Definition of Perpendicular-Bisector of a Segment
5. AB = CB  All points on the perpendicular-bisector of a segment are equidistant from the endpoints of the segment
6. Segment BD is congruent to Segment BD  Reflexive Property
7. Triangle ADB is congruent to Triangle CDB  SSS Postulate


Alternate Proof

1. Segment BD is an altitude of Triangle ABC, drawn to Segment AC  Given
2. Segment BD is perpendicular to Segment AC  Definition of Altitude
3. Angle BDA is congruent to Angle BDC  Perpendicular line form right angles; Right angles are congruent
4. AD = DC  Given
5. Segment BD is congruent to Segment BD  Reflexive Property
6. Triangle ADB is congruent to Triangle CDB  SAS Postulate