To prove: CD―∥BE― Given: The diagram: The line BE― bisects ∠DBA ∠3=∼∠1

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To prove: CD―∥BE― Given: The diagram:  The line BE― bisects ∠DBA ∠3=∼∠1

lamanocornudaW · Accepted Answer

Concept Used: Transitive property of congruence: if a=∼b and b=∼c, then a=∼c. Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. Consider the given figure:  It is given that, the line BE― bisects ∠DBA, this implies that, m∠DBE=m∠EBA m∠2=m∠3 That is, ∠2=∼∠3 Now applying the transitive property of congruence on ∠1=∼∠3 and ∠3=∼∠2, it can be said that ∠1=∼∠2 From the above figure, it can be observed that the angles ∠1 and ∠2 are the alternate interior angles which are formed when the lines CD― and BE― are cut by the transversal DB―. And since ∠1=∼∠2, so by the theorem 3-5, it can be said that the lines CD― and BE― are parallel.

Prove the congruence \overline{CD}\parallel\overline{BE}

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