Question
Kyle said that it is not possible to draw a trapezoid that is a rectangle. Trisha said it is possible. Who is correct?
Support your answer using the properties of sides and angles
Support your answer using the properties of sides and angles
Answers
GPT-4o mini
To determine who is correct between Kyle and Trisha regarding the possibility of a trapezoid being a rectangle, we need to analyze the definitions and properties of both shapes.
1. **Definition of a Trapezoid:** A trapezoid (or trapezium in some countries) is defined as a quadrilateral that has at least one pair of parallel sides. These parallel sides are referred to as the "bases" of the trapezoid.
2. **Definition of a Rectangle:** A rectangle is a specific type of quadrilateral that has four right angles (90 degrees) and opposite sides that are equal in length. Additionally, in a rectangle, the opposite sides are parallel.
Now, let's analyze the relationship between the two shapes:
- A rectangle has two pairs of parallel sides (the opposite sides), which also makes it a specific type of trapezoid because it has at least one pair of parallel sides.
- Since a rectangle also satisfies the condition of being a trapezoid by having parallel sides, we can conclude that every rectangle is, in fact, a trapezoid.
Given these definitions and properties, we can conclude that Trisha is correct. It **is** possible to have a trapezoid that is also a rectangle, as all rectangles fall under the broader category of trapezoids due to the presence of at least one pair of parallel sides. Kyle's assertion that it is not possible is therefore incorrect.
1. **Definition of a Trapezoid:** A trapezoid (or trapezium in some countries) is defined as a quadrilateral that has at least one pair of parallel sides. These parallel sides are referred to as the "bases" of the trapezoid.
2. **Definition of a Rectangle:** A rectangle is a specific type of quadrilateral that has four right angles (90 degrees) and opposite sides that are equal in length. Additionally, in a rectangle, the opposite sides are parallel.
Now, let's analyze the relationship between the two shapes:
- A rectangle has two pairs of parallel sides (the opposite sides), which also makes it a specific type of trapezoid because it has at least one pair of parallel sides.
- Since a rectangle also satisfies the condition of being a trapezoid by having parallel sides, we can conclude that every rectangle is, in fact, a trapezoid.
Given these definitions and properties, we can conclude that Trisha is correct. It **is** possible to have a trapezoid that is also a rectangle, as all rectangles fall under the broader category of trapezoids due to the presence of at least one pair of parallel sides. Kyle's assertion that it is not possible is therefore incorrect.