Similar Figures

Front

What are 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 in proportion.

Front

What is the definition of corresponding sides?

Back

Corresponding sides are the sides of similar figures that are in the same relative position. For example, in two similar triangles, the side lengths that correspond to each other are proportional.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is a proportion in the context of similar figures?

Back

A proportion is an equation that states that two ratios are equal. In similar figures, the ratios of the lengths of corresponding sides are equal.

Front

If two triangles have sides of lengths 3, 4, and 5 and 6, 8, and 10, are they similar?

Back

Yes, they are similar because the ratios of the corresponding sides (3:6, 4:8, 5:10) are all equal (1:2).

Front

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

Back

The height can be found using the proportion of corresponding sides. For example, if you know the height of a smaller figure and the corresponding side lengths, you can set up a proportion to find the unknown height.

Front

What does it mean to complete a proportion?

Back

Completing a proportion means finding the missing value in a ratio that makes the two ratios equal.

Front

What is the significance of the term 'scale factor' in similar figures?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures. It indicates how much larger or smaller one figure is compared to the other.

Front

Can two figures be similar if one is a reflection of the other?

Back

Yes, two figures can be similar even if one is a reflection of the other, as long as their corresponding angles are equal and their sides are proportional.

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 ratio of their corresponding side lengths.