Question

question 1 - 2
fill in the blanks using the available answer choices.
complete the proof.
given: bd bisects ac at point e; \\( \angle b a e \cong \angle d c e \\).
prove: \\( \triangle a b e \cong \triangle c d e \\).
we are given that bd bisects ac at point e and \\( \angle b a \\) segment addition postulate
because bd bisects ac at point e, \\( a e \cong c e \\) by the definition of a segment bisector. by the vertical angles theorem, \\( \angle a e b \cong \angle c e d \\). therefore, \\( \triangle a b e \cong \triangle c d b \\) by the
asa postulate.

Explanation:

Step1: Use the definition of a segment bisector

Since \(BD\) bisects \(AC\) at point \(E\), by the definition of a segment bisector, \(AE\cong CE\).

Step2: Use the Vertical Angles Theorem

By the Vertical Angles Theorem, \(\angle AEB\cong\angle CED\).

Step3: Use ASA (Angle - Side - Angle) Postulate

We are given \(\angle BAE\cong\angle DCE\), \(AE\cong CE\) (from step 1), and \(\angle AEB\cong\angle CED\) (from step 2). So, by the ASA Postulate, \(\triangle ABE\cong\triangle CDE\).

Answer:

\(\triangle ABE\cong\triangle CDE\) by the ASA Postulate.