Question
Which pair of non-congruent figures must be similar?
two squares
two parallelograms (not rectangles)
two right triangles
two isosceles triangles (not equilateral)
two squares
two parallelograms (not rectangles)
two right triangles
two isosceles triangles (not equilateral)
Answers
GPT-4o mini
To determine which pair of non-congruent figures must be similar, let's analyze each option:
1. **Two Squares**: Two squares that are of different sizes are congruent by definition (they have the same shape but different sizes). Hence, they cannot be non-congruent.
2. **Two Parallelograms (not rectangles)**: Two non-congruent parallelograms can have different angles or side lengths but still maintain the property of parallelograms. However, they do not necessarily have to be similar. For instance, one parallelogram could have a much more acute angle than the other, leading them to not be similar.
3. **Two Right Triangles**: Two right triangles can be non-congruent while still being similar as long as their corresponding angles are equal. For example, a right triangle with angles 30°, 60°, and 90° can be scaled to create a non-congruent triangle with the same angles.
4. **Two Isosceles Triangles (not equilateral)**: Two non-congruent isosceles triangles can have the same base angles, which would make them similar. However, if the angles are different, they may not be similar.
Based on the reasoning above, the pair that must be similar and can be non-congruent is:
**Two Right Triangles.**
1. **Two Squares**: Two squares that are of different sizes are congruent by definition (they have the same shape but different sizes). Hence, they cannot be non-congruent.
2. **Two Parallelograms (not rectangles)**: Two non-congruent parallelograms can have different angles or side lengths but still maintain the property of parallelograms. However, they do not necessarily have to be similar. For instance, one parallelogram could have a much more acute angle than the other, leading them to not be similar.
3. **Two Right Triangles**: Two right triangles can be non-congruent while still being similar as long as their corresponding angles are equal. For example, a right triangle with angles 30°, 60°, and 90° can be scaled to create a non-congruent triangle with the same angles.
4. **Two Isosceles Triangles (not equilateral)**: Two non-congruent isosceles triangles can have the same base angles, which would make them similar. However, if the angles are different, they may not be similar.
Based on the reasoning above, the pair that must be similar and can be non-congruent is:
**Two Right Triangles.**