SOLUTION: <pre> Given AD = AE, &#8736;ADE = &#8736;C Prove: DE &#8741; BC {{{drawing(200,200,-2,2,-1,3, locate(-1,0,B), locate(1,0,C), locate(-.7,.6,D), locate(.8,.6,E), locate(0,2.2

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Question 258010: 
Given AD = AE, ∠ADE = ∠C
Prove: DE ∥ BC

Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Do we know anything about anything else? The angle info was hiding
Do you mean (Picture shows triangle ADE is in triangle ABC)
Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!


Given AD = AE, ∠ADE = ∠C
Prove: DE ∥ BC




1. AD = AE                1. Given

2. ∆ADE is isosceles      2. Two sides equal

3. ∠ADE = ∠AED           3. Base angles of isosceles ∆ADE are equal

4. ∠ADE = ∠C             4. Given

5. ∠AED = ∠C             5. Angles equal to the same angle
                            are equal to each other. (Transitive
                            property of equivalence) (3 and 4)  

6. DE ∥ BC                6. Corresponding angles when transversal
                            AC cuts DE and BC

Edwin
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