Similar Figures & Scale Drawings

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 a scale drawing?

Back

A scale drawing is a representation of an object or a figure that is proportional to the actual size, using a specific ratio or scale.

Front

How do you find 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 length of 10 cm and a width of 5 cm, what is the perimeter?

Back

The perimeter is 30 cm (P = 2(length + width) = 2(10 + 5)).

Front

What happens to the perimeter of a shape when it is enlarged by a scale factor of 2?

Back

The perimeter doubles when the shape is enlarged by a scale factor of 2.

Front

If a rectangle is scaled down by a factor of 0.5, what happens to its area?

Back

The area is reduced to one-fourth of the original area because area scales by the square of the scale factor (0.5^2 = 0.25).

Front

How do you set up a proportion to find an unknown height using similar figures?

Back

Set up a proportion by equating the ratios of corresponding sides: height of object 1 / shadow of object 1 = height of object 2 / shadow of object 2.

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, what is the height of a building that casts a shadow of 24 feet?

Back

The height of the building is 32 feet (set up the proportion: 12/9 = x/24).

Front

What is the formula for the area of a rectangle?

Back

The area of a rectangle is calculated using the formula: Area = length × width.

Front

What is the relationship between the scale factor and the dimensions of similar figures?

Back

The dimensions of similar figures are proportional to the scale factor; if the scale factor is k, then each dimension is multiplied by k.