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Shape ABCD is a rectangle. Side AE and Side CE have equal measures, while Sides BE and DE also have equal measures. Use a two-column proof to show that Triangle AEB is congruent to Triangle CED. Remember to include headings for your proof.

Answer :

Triangle AEB is congruent to Triangle CED.

Proof:

Statement: Shape ABCD is a rectangle.

Reason: Given.

Statement: AE = CE.

Reason: Given.

Statement: BE = DE.

Reason: Given.

Statement: Angle AEB = Angle CED.

Reason: Vertical angles are congruent.

Statement: Side-Angle-Side (SAS) congruence criterion.

Reason: AE = CE (Given), BE = DE (Given), Angle AEB = Angle CED.

Statement: Triangle AEB = Triangle CED.

Reason: SAS congruence criterion (from the previous statement) by congruence definition.

Therefore, Triangle AEB is congruent to Triangle CED.

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