Question 175914
I'm assuming that the drawing looks like this (minus the labels of angles 1, 2, 3, and 4) Note: drawing is not to scale

<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/iso_tri.png" border="0" alt="Photobucket">

Here's a two column proof:
<table cellspacing="50">
<th>Statement</th><th>Reason</th>
<tr><td>1. Triangle WXZ is isoceles</td><td>Given</td></tr>
<tr><td>2. Point Y is the midpoint of segment XZE</td><td>Given</td></tr>
<tr><td>3. Segment WX = Segment WZ</td><td>Definition of Isosceles</td></tr>
<tr><td>4. Angle WXY = Angle WZY</td><td>Definition of Isosceles</td></tr>
<tr><td>5. Segment XY = Segment YZ</td><td>Definition of Midpoint</td></tr>
<tr><td>6. Triangle WXY = Triangle WYZ</td><td>SAS Property of Congruence</td></tr>
<tr><td>7. Angle XWY = Angle YWZ</td><td>CPCTC</td></tr>
<tr><td>8. Segment YW bisects Angle XWZ </td><td>Definition of Angle Bisector</td></tr>
</table>



Note: CPCTC = Corresponding Parts of Congruent Triangles are Congruent



Remember, the definition of an isosceles triangle is that the triangle has two equal sides and two equal base angles. Also, remember that if two angles are equal, and they form a larger angle, this means that they are the result of a angle bisection.