pe of AC = %3D -3-5 -8 1-(-7) %3D 1-1 = undefined ope of BD The line is vertical. %3D Since a horizontal and vertical line are perpendicular, the diagonals are perpendicular. Parallelogram ABCD is a square which is also a rhombus and a rectangle. Exercises Given each set of vertices, determine whether DABCD is a rhombus, rectangle, or square. List all that apply. Explain. 1. A(0, 2), B(2, 4), C(4, 2), D(2, 0) 2. A(-2, 1), B(-1, 3), C(3, 1), D(2, -1) 3. A(-2,-1), B(0, 2), C(2, -1), D0, -4) 4. А(-3, 0), B(—1, 3), С(6, -1), D(3, -4) 5. PROOF Write a two-column proof. Given: Parallelogram RSTU. RS ST Prove: RSTU is a rhombus.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Author:HOLT MCDOUGAL
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Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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### Understanding Quadrilaterals in Geometry

In geometry, analyzing the properties of quadrilaterals is essential for determining their specific classifications such as rhombus, rectangle, or square. Let's delve into some exercises that will help enhance your understanding of these concepts.

---

### Exercise: Classification of Quadrilaterals

Given each set of vertices, determine whether quadrilateral ABCD is a rhombus, rectangle, or square. List all that apply and provide explanations:

1. **Vertices:**
    - \( A(0, 2) \)
    - \( B(2, 4) \)
    - \( C(4, 2) \)
    - \( D(2, 0)\)
    
    **Explanation:**

2. **Vertices:**
    - \( A(-2, 1) \)
    - \( B(-1, 3) \)
    - \( C(3, 1) \)
    - \( D(2, -1)\)
    
    **Explanation:**

3. **Vertices:**
    - \( A(-2, -1) \)
    - \( B(0, 2) \)
    - \( C(2, -1) \)
    - \( D(0, -4)\)
    
    **Explanation:**

4. **Vertices:**
    - \( A(-3, 0) \)
    - \( B(-1, 3) \)
    - \( C(5, -1) \)
    - \( D(3, -4)\)
    
    **Explanation:**

---

### Proof: Understanding Rhombus Properties

5. **Proof Write a two-column proof.**
   - **Given:**
       - Parallelogram \( RSTU \)
       - \( RS \cong ST \)
   - **Prove:**
       - \( RSTU \) is a rhombus.
       
   \[
   \begin{array}{|c|c|}
   \hline
   \textbf{Statement} & \textbf{Reason} \\
   \hline
   & \\
   & \\
   & \\
   & \\
   & \\
   \hline
   \end{array}
   \]

#### Diagram Explanation:

- The provided diagram shows a parallelogram \( RSTU \) with diagonals that intersect
Transcribed Image Text:### Understanding Quadrilaterals in Geometry In geometry, analyzing the properties of quadrilaterals is essential for determining their specific classifications such as rhombus, rectangle, or square. Let's delve into some exercises that will help enhance your understanding of these concepts. --- ### Exercise: Classification of Quadrilaterals Given each set of vertices, determine whether quadrilateral ABCD is a rhombus, rectangle, or square. List all that apply and provide explanations: 1. **Vertices:** - \( A(0, 2) \) - \( B(2, 4) \) - \( C(4, 2) \) - \( D(2, 0)\) **Explanation:** 2. **Vertices:** - \( A(-2, 1) \) - \( B(-1, 3) \) - \( C(3, 1) \) - \( D(2, -1)\) **Explanation:** 3. **Vertices:** - \( A(-2, -1) \) - \( B(0, 2) \) - \( C(2, -1) \) - \( D(0, -4)\) **Explanation:** 4. **Vertices:** - \( A(-3, 0) \) - \( B(-1, 3) \) - \( C(5, -1) \) - \( D(3, -4)\) **Explanation:** --- ### Proof: Understanding Rhombus Properties 5. **Proof Write a two-column proof.** - **Given:** - Parallelogram \( RSTU \) - \( RS \cong ST \) - **Prove:** - \( RSTU \) is a rhombus. \[ \begin{array}{|c|c|} \hline \textbf{Statement} & \textbf{Reason} \\ \hline & \\ & \\ & \\ & \\ & \\ \hline \end{array} \] #### Diagram Explanation: - The provided diagram shows a parallelogram \( RSTU \) with diagonals that intersect
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