SOLUTION: Given : Line AD bisects angle BAC. Line AD bisects angle BDC Prove: Line AB is congruent to line AC

Algebra ->  Geometry-proofs -> SOLUTION: Given : Line AD bisects angle BAC. Line AD bisects angle BDC Prove: Line AB is congruent to line AC      Log On


   

Question 689206: Given : Line AD bisects angle BAC.
Line AD bisects angle BDC
Prove: Line AB is congruent to line AC
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Create a plan before tackling the proof. If you can prove line AD cuts the figure into two congruent triangles, then AB and AC are congruent (CPCTC). How can you prove congruent triangles? AD bisects BDC so angle BDA and angle CDA are congruent. AD is congruent to AD by the reflexive property. AD bisects BAC so angle BAD and angle CAD are congruent. That's two congruent angles and their included side congruent, or ASA, which means the triangles are congruent.


Now write the proof.


Line AD bisects angle BAC. ------Given

Line AD bisects angle BDC ------Given

AD congruent AD ------Reflexive property of equality.

Angle BDA congruent angle CDA ------- Def. of angle bisector.

Angle BAD congruent angle CAD ------- Def. of angle bisector.

Triangle BAD congruent to Triangle CAD ------ ASA

AB congruent AC --------CPCTC (corresponding parts of congruent triangles are congruent).

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)