Thank you for visiting Write a formal proof Given Rhombus ABCD Prove Triangle AEB is congruent to Triangle CEB. 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!
Answer :
Final answer:
By utilizing the properties of a rhombus and the SAS Postulate, we can formally prove that Triangle AEB is congruent to Triangle CEB. The equality of sides AE and CE, the shared side BE, and the right angles at E make the two triangles congruent.
Explanation:
The given problem involves a rhombus and the task is to prove that two triangles within the rhombus are congruent. To prove that Triangle AEB is congruent to Triangle CEB, we can use the following properties and theorems:
- In a rhombus, all sides are of equal length, so we have AB = BC = CD = DA.
- The diagonals of a rhombus bisect each other at right angles. So, diagonal BD bisects diagonal AC at E, and we have AE = CE and BE = DE. Also, angle AEB and angle CEB are right angles.
- By the definition of a rhombus, we can deduce that Triangle AEB and Triangle CEB are right triangles.
- SAS Postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
- By applying the SAS Postulate to Triangle AEB and Triangle CEB, we note that AE = CE, BE is common, and angle AEB is congruent to angle CEB as they are both right angles.
- Hence, by SAS Postulate, Triangle AEB is congruent to Triangle CEB.
Thank you for reading the article Write a formal proof Given Rhombus ABCD Prove Triangle AEB is congruent to Triangle CEB. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
