Question

complete the proof by selecting the correct reason to match the statement. given: $overline{ac}$ and $overline{bd}$ bisect each other. prove: $overline{bc}congoverline{ad}$. step statement reason 1 $ac$ and $bd$ bisect each other 2 $becong ed$ 3 $aecong ec$ 4 $angle beccongangle dea$ 5 $\triangle bcecong\triangle dae$ 6 $overline{bc}congoverline{ad}$ answer attempt 1 out of 2 step 1 reason = step 2 reason = step 3 reason = step 4 reason = step 5 reason = step 6 reason =

Explanation:

Step1: Given information

Given

Step2: Definition of bisect

Definition of segment - bisector (since \(BD\) is bisected, \(BE\cong ED\))

Step3: Definition of bisect

Definition of segment - bisector (since \(AC\) is bisected, \(AE\cong EC\))

Step4: Vertical - angles theorem

Vertical angles are congruent (\(\angle BEC\) and \(\angle DEA\) are vertical angles)

Step5: Side - Angle - Side (SAS) congruence postulate

\(BE\cong ED\), \(\angle BEC\cong\angle DEA\), \(AE\cong EC\), so \(\triangle BCE\cong\triangle DAE\) (SAS)

Step6: Corresponding parts of congruent triangles are congruent (CPCTC)

Since \(\triangle BCE\cong\triangle DAE\), \(BC\cong AD\) (CPCTC)

Answer:

Step 1 Reason = Given
Step 2 Reason = Definition of segment - bisector
Step 3 Reason = Definition of segment - bisector
Step 4 Reason = Vertical - angles theorem
Step 5 Reason = Side - Angle - Side (SAS) congruence postulate
Step 6 Reason = Corresponding parts of congruent triangles are congruent (CPCTC)