I tried
- BE bisects AD: This means that line BE divides line AD into two equal halves.
- AB || DE: This indicates that lines AB and DE are parallel.
To prove: AB DE
Statement Validate Reason
1. BE bisects AD Given Given
2. AB || DE Given Given
3. ∠ABE = ∠ADE Definition of angles When a line bisects another line, the two angles formed are equal.
4. ∠ADE = ∠ABE Symmetric property If two angles are equal, then their order can be reversed.
5. ΔABE ≅ ΔADE ASA congruence If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.
6. AB = DE Corresponding parts If two triangles are congruent, then their corresponding parts (including sides) are congruent.
By using the properties of parallel lines and the fact that BE bisects AD, we can prove that AB is equal to DE.