#8.1 Similar Polygons

Front

What are similar polygons?

Back

Polygons that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of 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 equal and the lengths of their corresponding sides are in proportion.

Front

What is the significance of the scale factor in similar polygons?

Back

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

Front

If two polygons are similar, how do you find the length of a side in one polygon if you know the corresponding side in the other polygon?

Back

Use the scale factor: if the scale factor is k, and you know the length of a side in the smaller polygon, multiply that length by k to find the corresponding side in the larger polygon.

Front

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

Back

The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths.

Front

If the sides of two similar polygons are in the ratio 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 4:9, since (2^2):(3^2) = 4:9.

Front

How can you find the value of x in similar polygons?

Back

Set up a proportion using the lengths of corresponding sides and solve for x.

Front

What is a proportion in the context of similar polygons?

Back

A proportion is an equation that states that two ratios are equal, often used to relate the lengths of corresponding sides of similar polygons.

Front

What is the formula for finding the area of a polygon?

Back

The area of a polygon can be calculated using various formulas depending on the type of polygon, such as A = 1/2 * base * height for triangles or A = side^2 for squares.

Front

What role do corresponding angles play in determining similarity?

Back

Corresponding angles must be equal for two polygons to be considered similar.