Given: segment AE and segment CD are lines. Prove: angle ABD is congruent to angle CBE.
You need to give more information. With just what you have, it's easy to construct a diagram with points A,B,C,D,E where the angles are not congruent.
To prove that angle ABD is congruent to angle CBE, we need to show that they have the same measure or size. One way to do this is to use the concept of vertical angles.
Vertical angles are formed by two intersecting lines, where the angles opposite each other are congruent. In this case, since segment AE and segment CD are lines, they intersect at point B. So, angles ABD and CBE are vertical angles.
To fully prove the congruence of angle ABD and angle CBE, we need to show that these two angles are vertical angles.
Proof:
1. Given: segment AE and segment CD are lines.
2. Draw lines AE and CD intersecting at point B.
3. Define angle ABD and angle CBE as the angles formed by the intersecting lines at point B.
4. Since segment AE and segment CD are lines, they intersect at point B.
5. By definition, angles ABD and CBE are vertical angles.
6. By the Vertical Angle Theorem, vertical angles are congruent.
7. Therefore, angle ABD is congruent to angle CBE.
By proving that angles ABD and CBE are vertical angles, we can conclude that they are congruent.