SOLUTION: Could you please help me write an INDIRECT PROOF for this problem? <a rel=nofollow HREF="https://ibb.co/RNF82yf"><img src="https://i.ibb.co/gd2YyVN/IMG-4952-indirect-proof.jpg"

Click here to see ALL problems on Geometry proofs

Question 1186350: Could you please help me write an INDIRECT PROOF for this problem?

Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

It's rather bizarre to ask for an indirect proof, since a direct proof is so easy.

But if that's what you need, we can do it that way.
BC and DC are not congruent assumption AB is congruent to AD given angle ABC is congruent to angle DAC given angle B is congruent to angle D angles opposite congruent sides are congruent triangle BAC is congruent to triangle DAC Angle-Side-Angle BC is congruent to DC corresponding parts of congruent triangles

That contradicts the assumption, so the assumption is false; BC is congruent to DC

Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!

Assume BC is not congruent to DC. 1. AB ≅ AD | given 2. ∠BAC ≅ ∠DAC | given 3. AC ≅ AC | reflexive property of equality 4. △BAC ≅ △DAC | Side-angle-side (SAS) 5. BC ≅ DC | Corresponding parts of congruent triangles. (CPCT) 6. BC ≅ DC | 5 contradicts the assumption that BC is not congruent to DC. Notice: the theorem was not proved at step 5, because 5 was deduced under the assumption BC is not congruent to DC. The theorem was not proved there. It was only proved by the statement 6 that the assumption leads to a contradiction. Edwin