# How to Write a Statement of Similarity in Geometry

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Similarity is one of the major topics covered in introductory geometry courses. Saying that two shapes are similar means that they have the same angles and ratio of side lengths but they are not the same size. In other words, the smaller shape is like a miniature version of the larger shape. Similarity is useful in many geometry proofs, and so students need to learn how to write a proper statement of similarity.

• Identify two shapes that are similar.

• Draw both shapes in the same orientation so that the congruent angles line up with each other. This usually involves rotating one of the shapes. For example, if you have two similar right triangles, you could draw both so that the right angle is facing the lower left-hand corner of the page and the smallest angle is pointing toward the lower right-hand corner.

• Label the vertices of the triangles according to the original figure.

• Choose a pair of congruent angles and write the letter names of those two angles on a piece of paper about one inch apart.

• Choose a second pair of congruent angles and write the letter names of those two angles immediately to the right of the two letters from Step 4. Write them in the same order so that adjacent letters belong to the same triangle.

• Write the letter names of the third pair of congruent angles immediately to the right of the two letters from Step 5. Write them in the same order so that adjacent letters belong to the same triangle.

• Write three short horizontal lines between the three triplets of letters. This is the similarity sign in geometry and it looks like an equals sign with an extra line. A second sign for similarity is the "~" symbol.

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