Question

Can anyone help? 2/5

Answer 1

Answer:

Statements                                                     Reasons

1.  ∠ AED ~∠ CEB                                      1. Given

                                                                   

2. AD ║ BC                                               2. Line AD is equal to line BC and

                                                                   base angles B and C are equal  

3. ∠ADE ∠ CBD                                        3.∠ADE is alternate to ∠ CBD and

                                                                      thus equal  

4.   ∠ABD≅ ∠ DEC                                     4. Alternate interior  are  

    ∠BEA ≅ ∠CED                                           congruent (Alt. int. ∠s)

5.  ∠ AED ~∠ CEB                                       5. AAS (Angle Angle Side)

6. ABCD is a                                                 6. Definition of a trapezoid

trapezoid

Explanation:

A trapezoid is a quadrilateral with at least  one pair  parallel side

Statements                                                     Reasons

1.  ∠ AED ~∠ CEB                                      1. Given

                                                                   

2. AD ║ BC                                               2. Line AD is equal to line BC and

                                                                   base angles B and C are equal  

3. ∠ADE ∠ CBD                                        3.∠ADE is alternate to ∠ CBD and

                                                                      thus equal  

4.   ∠ABD≅ ∠ DEC                                     4. Alternate interior  are  

    ∠BEA ≅ ∠CED                                           congruent (Alt. int. ∠s)

5.  ∠ AED ~∠ CEB                                       5. AAS (Angle Angle Side)

6. ABCD is a                                                 6. Definition of a trapezoid

trapezoid

Answer 2

Answer:

These are the statements and reasons that complete the proof:

1. ABCD is a trapezoid.          

2. AD || BC.                         2. The two bases of a trapezoid are parallel.

3. ∠ ADE ≅ ∠ CBD.             3. Alternate interior angles are congruent.

4. ∠ BDA  ≅ ∠ CAD

Explanation:

Kindly, note that you should have submitted the word bank.

1. In the first blank, you must write ABCD is trapezoid.

The reason is that it is the information given.

What is given is always the first statment of a  two-column geometric proof.

Next you must use deductions using theorems or postulates.

2. In the second blank, you must write AD || BC.

That means that the segment AD is paralled to the segment BC.

In the next blank on that same row, you must write "The two bases of a trapezoid are parallel", which is the definition of a trapezoid.

3. In the first column of the third row you must complete the statement:

• ∠ ADE ≅ ∠ CBD

The reason, which you must write on the right cel, is that alternate interior angles formed by parallel lines are congruent (just as it says in the last cell shown).

Thus, in the next cell you must write the reason: Alternate interior angles are congruent.

4. In the first cell of the fourth row you must write

• ∠ BDA  ≅ ∠ CAD

Because that is the other pair of interior angles formed by the two parallel lines.

Since you have proven that two pairs of angles are congruent, you conclude that the two triangles are similar by the AA postulate (Angle - Angle similarity postulate).