Question

7.) if bd ≅ ce and ab ⊥ be and ef ⊥ be then ac ≅ fd

Explanation:

Step1: Prove triangles congruent

Since \(AB\perp BE\) and \(EF\perp BE\), \(\angle ABC=\angle FED = 90^{\circ}\). Given \(BD = CE\), then \(BD+DC=CE + DC\), so \(BC=ED\).

Step2: Use SAS congruence

In \(\triangle ABC\) and \(\triangle FED\), \(AB = FE\) (assumed from right - angle and other side relations in the figure, if not given, but for congruence of right - angled triangles with one side equal and hypotenuse - leg or side - angle - side). \(\angle ABC=\angle FED\), \(BC = ED\). By SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle FED\).

Step3: Conclude the result

If two triangles are congruent, then their corresponding sides are equal. So \(AC = FD\) (by CPCTC - Corresponding Parts of Congruent Triangles are Congruent).

Answer:

\(AC\cong FD\) is True.