Question

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AEC ≅ DEB, given that CA is parallel to DB and E is the midpoint of AD. Submit the entire proof to your instructor.
Given:
CA || DB
E is the midpoint of AD
Prove:
AEC ≅ DEB

Answer 1

Answer:

1.∠1 and ∠2 are supplementary angles........... 1. Given

2. m∠1 + m∠2 = 180° ........................... 2. Definition of Supplementary Angles

3. ∠1 and ∠3 are supplementary angles.......... 3. Exterior sides in opposite rays

4. m∠1 + m∠3 = 180°.......................................4. (Angles forming a linear pair sum to 180° )

5. m∠1 + m∠2 = m∠1 + m∠3........................ 5. ( Transitive Property of Equality)

6. ( m∠2 =m∠3)..............................................6. (Algebra)

7. l || m ............................................................7. (Converse of Corresponding Angles Postulate)

Answer 2

A two column proof for ΔAEC ≅ ΔDEB  is as shown below.

What are congruent triangles?

"Two triangles are congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure."

What are interior angles?

"These angles formed on the inside of two straight lines when crossed by a transversal."

What is midpoint?

"It is point which divides a line segment into two equal parts."

What is AAS postulate of triangle congruence?

"AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent."

For given question,

Given that CA is parallel to DB and E is the midpoint of AD.

CA is parallel to DB

CB is transversal.

∠ACB and ∠CBD are alternate interior angles.

We know that when a transversal intersects a parallel line then alternate interior angles formed are congruent.

So, ∠ACB ≅ ∠CBD                       ................(i)

Similarly for CA || DB and AD is transversal.

∠CAD ≅ ∠ADB                             ..................(ii)

Also,  E is the midpoint of AD.

By definition of midpoint,

⇒ AE = ED                                      ..................(iii)

From (i), (ii) and (iii),

By AAS postulate of triangle congruence,

ΔAEC ≅ ΔDEB      

Therefore, a two column proof for ΔAEC ≅ ΔDEB  is as shown below.

Learn more about AAS postulate of triangle congruence here:

https://brainly.com/question/1593616

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