Similar Figures

Front

What is the definition of similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

How do you determine if two polygons are similar?

Back

Two polygons are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

Front

What is the formula for finding the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

If a rectangle has a width of 18 in. and a length of 24 in., what is the scale factor if the width is enlarged to 54 in.?

Back

The scale factor is 3, since 54 in. (new width) divided by 18 in. (original width) equals 3.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the scale factor.

Front

If the scale factor between two similar triangles is 2, what is the ratio of their areas?

Back

The ratio of their areas is 4, since 2 squared equals 4.

Front

How can you use a mirror to find the height of an object?

Back

By standing at a distance from the mirror and adjusting your position until you can see the top of the object in the mirror, you can use similar triangles to calculate the height of the object.

Front

What is the height of a tree if you see its reflection in a mirror placed on the ground and the distance from the mirror to the tree is 72 feet?

Back

The height of the tree is 72 feet, assuming the observer's eye level is at the same height as the mirror.

Front

What does it mean for sides to be proportional?

Back

Sides are proportional when the ratios of the lengths of corresponding sides of two figures are equal.

Front

If two similar figures have a scale factor of 3, what is the relationship between their corresponding side lengths?

Back

The corresponding side lengths of the larger figure are three times the lengths of the corresponding sides of the smaller figure.