SOLUTION: Could you please help write an INDIRECT PROOF for this problem? My child is currently learning Indirect proofs at school. Would greatly appreciate your help. <a rel=nofollow HR

Algebra ->  Geometry-proofs -> SOLUTION: Could you please help write an INDIRECT PROOF for this problem? My child is currently learning Indirect proofs at school. Would greatly appreciate your help. <a rel=nofollow HR      Log On


   

Question 1186429: Could you please help write an INDIRECT PROOF for this problem? My child is currently learning Indirect proofs at school. Would greatly appreciate your help.
IMG-4971-indirectproof2
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
< BAC is not congruent to <DAC
AB=AD
prove:
BC is not congruent+DC
guidelines for writing indirect proof:
1. identify the statement that you want to prove is true
2. begin by assuming the statement is false, assume its opposite is true
3. obtain statements that are logically follow from your assumption
4. if obtain contradiction, then the original statement must be true


statement......................................................reason
1. < BAC is not congruent to <DAC.............given
2.+AB=AD.....................................................given
3. BC is congruent DC.....................................indirect proof assumption
4. C is midpoint of+BD....................................definition of midpoint
5. AC is bisector of <ABC...............................definition of bisector
6. < BAC is congruent to <DAC....................reflexive property
7. contradiction (3,6)...........................................the assumption is false


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Statement 5 in the response from the other tutor is not valid....
1. BC is congruent to DC                indirect proof assumption
2. AB is congruent to AD                given
3. AC is congruent to AC
4. Triangles ACB and ACD are congruent  SSS
5. Angles BAC and DAC are congruent     corresponding parts of congruent triangles

Statement 5 contradicts the given information that angles BAC and DAC are not congruent, so the assumption that BC is congruent to DC is false.

Therefore, BC is not congruent to DC, and the indirect proof is complete.