Question

Given: AD BC and AD || BC
Provę: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
A
reflexive property
alternate interior angles theorem
B
Statements
1. AD BC
✓ 2. ZDAC and BCA
are alt. interior angles
3. AD || BC
Reasons
1. given
2. def. of alt. interior angles
D
.
3. given
С
Correct Assemble the next
statement

Answer 1

It has been proven that ABCD is a parallelogram by using the single opposite side pair theorem.

What is a parallelogram?

A parallelogram can be defined as a type of polygon (quadrilateral) that has two equal pairs of parallel sides.

The single opposite side pair theorem.

Basically, the opposite sides of a parallelogram ABCD are always equal and as such we have:

• AB = DC

• AD = BC

Also, if a pair of opposite sides of a polygon (quadrilateral) is both congruent and parallel, then it is considered as a parallelogram based on the following:

1. AD≅BC               $\rightarrow$              (given)
2. AD║BC              $\rightarrow$               (given)
3. ∠DAC and ∠BCA are alternate interior angles $\rightarrow$  (def. of alt. interior angles).
4. ∠DAC ≅ ∠BCA   $\rightarrow$      (alternate interior angle theorem).
5. AC ≅ AC        $\rightarrow$           (reflexive property).
6. ΔDAC ≅ ΔBCA     $\rightarrow$             (side-angle-side = SAS).
7. AB ≅ CD             $\rightarrow$              (CPCTC = corresponding parts of congruent triangles are congruent).
8. ABCD is a parallelogram     $\rightarrow$       (parallelogram side theorem)

Read more on parallelogram here: https://brainly.com/question/4459854

Answer 2

Answer:in the image I added

Explanation: