Similarity

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the relationship between two shapes that have the same shape but may differ in size. This means that their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for 'Side-Side-Side Similarity', which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the AA~ criterion for triangle similarity?

Back

AA~ stands for 'Angle-Angle Similarity', which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

How do you find the scale factor between two similar triangles?

Back

The scale factor is found by taking the ratio of the lengths of corresponding sides of the two triangles. For example, if the length of a side in triangle ABC is 4 and the corresponding side in triangle DEF is 2, the scale factor from ABC to DEF is 1/2.

Front

What is a proportion in mathematics?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How can you determine if two triangles are similar using the SSS criterion?

Back

To determine if two triangles are similar using the SSS criterion, measure the lengths of the corresponding sides of both triangles and check if the ratios of the lengths are equal.

Front

What is the relationship between the heights of similar triangles?

Back

The heights of similar triangles are also in proportion to the lengths of their corresponding sides. If the scale factor of the sides is k, then the heights will also be in the ratio k.

Front

How can mirrors be used to measure the height of tall objects?

Back

Mirrors can be used to measure the height of tall objects by creating similar triangles. By standing at a distance and using the reflection of the object in the mirror, you can set up a proportion to find the height.

Front

What is the formula for finding the height of an object using similar triangles?

Back

The height of the object can be found using the formula: (height of object)/(distance from object) = (height of observer)/(distance from observer to mirror). This sets up a proportion based on similar triangles.

Front

What is the significance of corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal. This is a key property that helps establish the similarity of triangles.