Similarity (geometry) facts for kids
Similarity in geometry is a cool idea! It means that two shapes, like polygons (shapes with many straight sides), line segments, or other figures, can become exactly the same if you just make one bigger or smaller. Think of it like zooming in or out on a picture!
Similar objects don't have to be the same size. For two shapes to be similar, two things must be true:
- Their angles must have the same measurements.
- Their sides must be proportional. This means if you divide the length of one side of the first shape by the length of the matching side of the second shape, you'll always get the same number.
Some shapes are always similar. For example, any two circles are similar. Any two squares are also similar. And any two line segments are always similar too! When we say figure F is similar to figure F', we write it like this: F ~ F'.
Why Triangles Are Special
Triangles are a bit unique when it comes to similarity. For most shapes, you need both the angles to be equal AND the sides to be proportional for them to be similar. But for triangles, you only need one of these conditions to be true!
- If all the angles of one triangle are equal to the angles of another triangle, then the triangles are similar.
- If all the sides of one triangle are proportional to the sides of another triangle, then the triangles are also similar.
This makes working with similar triangles a bit easier than other shapes!
Similarity vs. Congruence
Similarity is very close to another idea called congruence. When two shapes are congruent, it means they are exactly the same size and shape. You can move, rotate, or flip one congruent shape, and it will perfectly fit on top of the other.
Think of it this way:
- Congruent shapes are like two identical cookies from the same batch. They are the same size and shape.
- Similar shapes are like a small cookie and a large cookie from the same cookie cutter. They have the same shape, but different sizes.
Because congruent shapes have the same sides and angles, they are always similar. But similar shapes are not always congruent, because they can be different sizes.
Images for kids
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Similar rectangles
