(ostion Watch Vide
hoose ALL answers that describe the quadrilateral if , and diagonals are perpendicular: .
Answer Attempt out of 2
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
stbmansmer

Ask by Weber Coles. in the United States

Jan 27,2025

Question

(ostion Watch Vide
hoose ALL answers that describe the quadrilateral if , and diagonals are perpendicular: .
Answer Attempt out of 2
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
stbmansmer

Ask by Weber Coles. in the United States

Jan 27,2025

UpStudy AI · Accepted Answer

To determine which quadrilaterals $$ G H I J $$ can be described based on the given conditions, let's analyze each property step-by-step.

### Given:
1. **Parallel Sides**: $$ \overline{G H} \parallel \overline{I J} $$
2. **Equal Lengths**: $$ G H = I J $$
3. **Perpendicular Diagonals**: $$ \overline{G I} \perp \overline{H J} $$

### Options to Consider:
1. Parallelogram
2. Rectangle
3. Rhombus
4. Square
5. Trapezoid

### Analysis:

1. **Parallelogram**:
   - **Definition**: Both pairs of opposite sides are parallel.
   - **Given Conditions**: Only one pair ($$ \overline{G H} \parallel \overline{I J} $$) is specified as parallel.
   - **Conclusion**: Not necessarily a parallelogram unless the other pair is also parallel.
   
2. **Rectangle**:
   - **Definition**: Opposite sides are equal and parallel, and all angles are right angles.
   - **Diagonals**: In a rectangle, diagonals are equal but **not** perpendicular.
   - **Given Conditions**: Diagonals are perpendicular.
   - **Conclusion**: **Cannot** be a rectangle.

3. **Rhombus**:
   - **Definition**: All sides are equal in length, and opposite sides are parallel.
   - **Diagonals**: Diagonals are **perpendicular**.
   - **Given Conditions**: Satisfies all conditions (since $$ G H = I J $$ and diagonals are perpendicular).
   - **Conclusion**: **Yes**, it can be a rhombus.

4. **Square**:
   - **Definition**: All sides are equal, opposite sides are parallel, and all angles are right angles.
   - **Diagonals**: Diagonals are both **equal** and **perpendicular**.
   - **Given Conditions**: Satisfies all conditions.
   - **Conclusion**: **Yes**, it can be a square.

5. **Trapezoid**:
   - **Definition**: At least one pair of opposite sides is parallel.
   - **Given Conditions**: Only one pair is specified as parallel, and diagonals are perpendicular.
   - **Diagonal Constraint**: Standard trapezoids do **not** have perpendicular diagonals unless they fit into more specific categories like an isosceles trapezoid with additional properties.
   - **Conclusion**: Generally, **no**, it isn't a trapezoid under given conditions.

### **Final Answer:**
The quadrilateral $$ G H I J $$ can be described as both a **Rhombus** and a **Square** based on the given properties.

**Correct Choices:**
- Rhombus
- Square
The quadrilateral $$ G H I J $$ is both a rhombus and a square.

(ostion Watch Vide
hoose ALL answers that describe the quadrilateral if , and diagonals are perpendicular: .
Answer Attempt out of 2
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
stbmansmer

Upstudy AI Solution

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(ostion Watch Vide hoose ALL answers that describe the quadrilateral if , and diagonals are perpendicular: . Answer Attempt out of 2 Parallelogram Rectangle Rhombus Square Trapezoid stbmansmer

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(ostion Watch Vide
hoose ALL answers that describe the quadrilateral if , and diagonals are perpendicular: .
Answer Attempt out of 2
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
stbmansmer