Question 258010

<pre><font size = 4 color = "indigo"><b>
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,A),

triangle(-1,0,0,2,1,0), triangle(-.7,.6,0,2,.7,.6) )}}}

1. AD = AE                1. Given

2. &#8710;ADE is isosceles      2. Two sides equal

3. &#8736;ADE = &#8736;AED           3. Base angles of isosceles &#8710;ADE are equal

4. &#8736;ADE = &#8736;C             4. Given

5. &#8736;AED = &#8736;C             5. Angles equal to the same angle
                            are equal to each other. (Transitive
                            property of equivalence) (3 and 4)  

6. DE &#8741; BC                6. Corresponding angles when transversal
                            AC cuts DE and BC

Edwin</pre>