135k views
5 votes
Given: E is the midpoint of AB and CD little help please would be great

Given: E is the midpoint of AB and CD little help please would be great-example-1
User AllenJB
by
8.0k points

1 Answer

2 votes

You need to prove that ΔAEC ≅ ΔBED

You know that point E is the midpoint of AB and CD

The midpoint divides a line segment into two congruent lines. This means that E divides AB into two congruent segments AE and EB, and it also divides CD into two congruent segments CE and ED, then we can conclude that:

1. AE=EB → Reason Midpoint Theorem

2. CE=ED → Reason Midpoint theorem

Both lines AB and CD intersect at point E, forming an X shape. The ingles formed inside the X are vertically opposite angles, this means that

3. ∠AEC= ∠BED → Reason Vertically opposite angles

Since E is the midpoint where both "diagonals of the parallelogram" AB and CD intersect, then sides AC and DB are parallel. If AB || CD, then ∠ACE and ∠BDE are alternate interiors angles as well as ∠CAE and ∠DBE. Alternate interior angles are congruent, so that:

4. ∠ACE=∠BDE → Reason alternate interior angles, AB || CD

5. ∠CAE=∠DBE → Reason alternate interior angles, AB || CD

Then → ΔAEC ≅ ΔBED by SAS and AAA

User Kaunteya
by
9.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories