College

Thank you for visiting Given Diagonals AC and BD intersect at E in parallelogram ABCD Prove Triangle AEB is congruent to triangle CED. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Given: Diagonals AC and BD intersect at E in parallelogram ABCD.
Prove: Triangle AEB is congruent to triangle CED.

Answer :

Final answer:

To prove that triangle AEB is congruent to triangle CED, we can use the SAS (Side-Angle-Side) congruence criteria. By showing that the corresponding sides and the included angle are congruent, we can establish the congruence between the two triangles.

Explanation:

To prove that triangle AEB is congruent to triangle CED, we can use the SAS (Side-Angle-Side) congruence criteria. Here are the steps:

  1. Since AC and BD are diagonals of parallelogram ABCD, they bisect each other at point E.
  2. Therefore, AE = EC and BE = ED (Diagonals of a parallelogram bisect each other).
  3. We also know that AB and CD are opposite sides of the parallelogram, so they are congruent: AB = CD.
  4. Now, we have two pairs of corresponding sides that are congruent: AE = EC and BE = ED.
  5. Finally, we have the included angle AEB = CED (angle between corresponding sides).
  6. By the SAS congruence criteria, triangle AEB is congruent to triangle CED.

Thank you for reading the article Given Diagonals AC and BD intersect at E in parallelogram ABCD Prove Triangle AEB is congruent to triangle CED. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions