Determine whether each statement is always, sometimes, or never true.
Two cones are similar.
A pyramid is similar to a square.
Two spheres with the same radius are congruent.
Non-similar solids have different volumes.
two cones are similar= always
A pyramid is similar to a square. = never true
Two spheres with the same radius are congruent. = always trues
Non-similar solids have different volumes. =sometimes true
To determine whether each statement is always, sometimes, or never true, we need to consider the definitions and properties of the given geometric shapes.
1. Two cones are similar: Sometimes true. Two cones are similar if their corresponding dimensions (such as height and base radius) are proportional. However, it's important to note that not all cones are similar, as the dimensions can vary.
2. A pyramid is similar to a square: Never true. A pyramid is a three-dimensional solid, while a square is a two-dimensional shape. Thus, they cannot be similar since they belong to different categories.
3. Two spheres with the same radius are congruent: Always true. Two spheres with the same radius will have identical shapes and sizes, making them congruent.
4. Non-similar solids have different volumes: Always true. Similarity in geometric solids means their corresponding dimensions are proportional. When two solids are not similar, their dimensions are not proportional, resulting in different volumes.