Thread: Prove Angle 1 is = Angle 2

1. .

2. Re: Prove Angle 1 is = Angle 2

Hello, SmokeDawg!

Given: . $AB = AE,\; BC = DE.$
Prove: . $\angle 1 = \angle 2$

Code:
A
*
** **
* *   * *
*  *     *  *
*   *       *   *
*    *         *    *
*     *           *     *
*      * 1         2 *      *
*   *   *   *   *   *   *   *   *
B       C               D       E
$\begin{array}{cc cc cc}1. & AB = AE && 1. & \text{given} \\ 2. & \Delta ABE\text{ is isosceles} && 2. & \text{d{e}f. isosceles} \\ 3. & \angle B = \angle E && 3. & \text{"base angles"} \\ 4. & BC = DE && 4. & \text{Given} \\ 5. & \Delta ABC \cong \Delta AED && 5. & s.a.s. \\ 5. & AC = AD && 5. & \text{corres. parts} \\ 6. & \Delta ACD\text{ is isosceles} && 6. & \text{d{e}f. isosceles} \\ 7. & \angle 1 = \angle 2 && 7. & \text{"base angles"} \end{array}$