Thank you for visiting ABCD is a rhombus and side AE is congruent to side EC Prove that 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 :
ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
What is a rhombus?
A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given that the side AE is congruent to EC of rhombus.
That means, AE ≅ EC.
And the diagonals of rhombus bisects each other.
Both the triangle AEB and triangle CEB share the same side which is BE.
That means BE ≅ BE, by the reflexive property.
And the sides AB and BC are the sides of rhombus.
So, AE ≅ BC.
Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
To learn more about the rhombus;
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Final answer:
To prove triangle AEB is congruent to triangle CEB, we use the properties of a rhombus, given AE congruent to EC, and the SAS congruency theorem; by showing two sides and the included angle are respectively congruent.
Explanation:
In order to prove that triangle AEB is congruent to triangle CEB in a rhombus ABCD with AE congruent to EC, we will rely on the properties of a rhombus and congruency theorems.
One property of a rhombus is that its diagonals bisect each other at right angles. Given this property, and that AE is congruent to EC by given information, we can infer that triangle AEB and CEB share the following congruencies:
- Side AE is congruent to side EC by assumption.
- Side BE is common to both triangles AEB and CEB.
- Angles AEB and CEB are congruent since they are vertical angles.
Using the Side-Angle-Side (SAS) congruency theorem, we can determine that triangles AEB and CEB are congruent because they have one side and two adjacent angles that are respectively congruent.
