Similarity and Proportions

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the definition of proportionality in geometry?

Back

Proportionality in geometry refers to the relationship between two quantities where their ratio remains constant. If two figures are similar, the ratios of their corresponding side lengths are equal.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

How do you find the missing side length in similar figures?

Back

To find the missing side length in similar figures, set up a proportion using the lengths of the corresponding sides of the figures.

Front

What is the formula for setting up a proportion between two similar triangles?

Back

If triangle ABC is similar to triangle DEF, then the proportion can be set up as: AB/DE = BC/EF = AC/DF.

Front

If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF is similar to triangle ABC with a side length of 6, what is the length of the corresponding side in triangle DEF?

Back

The corresponding side in triangle DEF is 8. (Using the ratio 6/3 = 2, multiply the other sides by 2: 4*2 = 8.)

Front

What is the scale factor in similar figures?

Back

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

Front

If the scale factor of two similar polygons is 2:3, what does this mean?

Back

This means that for every 2 units in one polygon, there are 3 units in the corresponding side of the other polygon.

Front

How can you determine if two polygons are similar?

Back

Two polygons are similar if their corresponding angles are equal and the lengths of their corresponding 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.