Given: Circle X with radius r and circle Y with radius s. Prove: Circle X is similar to circle Y.
Statements
1. Translate X to Y
2. Circle X circle Y
3. Circle with center X has radius r
4. Circle with center Y has radius s
Reasons
5. x r
6. Y
7. S
Assemble the proof by dragging tiles to the Statements and Reasons columns.
Answer (1)
To prove that Circle X is similar to Circle Y, we need to understand that two circles are always similar, regardless of their sizes, because they have the same shape but different sizes. This property stems from the fact that all circles have the same angle measurements and their radii can be scaled versions of one another.
Here's a step-by-step explanation of the proof:
Statement: Translate Circle X to Circle Y. Reason: All circles centered at different points are congruent when a proper translation is applied.
Statement: Circle X has a defined radius of r . Reason: This is given by the problem.
Statement: Circle Y has a defined radius of s . Reason: This is also given by the problem.
Statement: Circle X is similar to Circle Y. Reason: By definition, all circles are similar because they can be transformed into each other by scaling, which involves multiplying the radius of one circle by a scalar value to achieve the radius of the other circle. In other words, if you multiply r by r s , you get s , which is a demonstration of similarity as the shape remains unchanged.
In conclusion, the concept of similarity between circles is based on the fact that all circles can be scaled to match one another's size without changing shape. Therefore, Circle X is similar to Circle Y by this property.
