I have to prove it by doing a statement and reason chart, as seen below. **Proving Parallelograms: Example Problem**In this example, we are given certain angle relationships and are asked to prove that a quadrilateral is a parallelogram based on these relationships.**Problem Statement:**Given:1. $ \angle A $ and $ \angle B $ are supplementary.2. $ \angle A $ is adjacent to $ \angle D $.To Prove: $ ABCD $ is a parallelogram, given that $ AB \cong CD $ (AB is congruent to CD).**Diagram Explanation:**On the right side of the notebook sheet, there is a diagram of the quadrilateral ABCD. Here is a breakdown of the diagram:- Quadrilateral $ABCD$ is drawn, indicating points $A$, $B$, $C$, and $D$.- Sides $AB$ and $CD$ are marked to indicate that they are equal in length (denoted by the congruency symbol $ \cong $).**Proof Structure:**A two-column proof structure will be used to demonstrate this mathematical proof. The two columns will be labeled "Statement" and "Reason" respectively.```| Statement | Reason ||-----------|--------|| 1) | 1) given |```**Explanation:**1. The given information forms the basis of the proof.2. $ \angle A $ and $ \angle B $ are supplementary, meaning their sum is 180 degrees.3. $ \angle A $ is adjacent to $ \angle D $.Using these angle relationships and the property that opposite sides of a parallelogram are equal in length, we will show that $ ABCD $ must be a parallelogram.**Note:**This problem and proof are intended for educational purposes to illustrate how angle and side relationships can be used to determine that a quadrilateral is a parallelogram. Further steps and justifications (not shown here) would complete the proof in a typical classroom setting.

Answered: D. 2) Given: LA LB Supplamentans SA; LD…

D. 2) Given: LA LB Supplamentans SA; LD a paratletogram B. prove: ABCDIS parallelogram ABICD Statement Reason ) given. CA TWAI SI

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

I have to prove it by doing a statement and reason chart, as seen below.

**Proving Parallelograms: Example Problem**

In this example, we are given certain angle relationships and are asked to prove that a quadrilateral is a parallelogram based on these relationships.

**Problem Statement:**

Given:
1. $ \angle A $ and $ \angle B $ are supplementary.
2. $ \angle A $ is adjacent to $ \angle D $.

To Prove: $ ABCD $ is a parallelogram, given that $ AB \cong CD $ (AB is congruent to CD).

**Diagram Explanation:**

On the right side of the notebook sheet, there is a diagram of the quadrilateral ABCD. Here is a breakdown of the diagram:

- Quadrilateral $ABCD$ is drawn, indicating points $A$, $B$, $C$, and $D$.
- Sides $AB$ and $CD$ are marked to indicate that they are equal in length (denoted by the congruency symbol $ \cong $).

**Proof Structure:**

A two-column proof structure will be used to demonstrate this mathematical proof. The two columns will be labeled "Statement" and "Reason" respectively.

```
| Statement | Reason |
|-----------|--------|
| 1) | 1) given |
```

**Explanation:**

1. The given information forms the basis of the proof.
2. $ \angle A $ and $ \angle B $ are supplementary, meaning their sum is 180 degrees.
3. $ \angle A $ is adjacent to $ \angle D $.

Using these angle relationships and the property that opposite sides of a parallelogram are equal in length, we will show that $ ABCD $ must be a parallelogram.

**Note:**
This problem and proof are intended for educational purposes to illustrate how angle and side relationships can be used to determine that a quadrilateral is a parallelogram. Further steps and justifications (not shown here) would complete the proof in a typical classroom setting.

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