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 area that is proportionally reduced or enlarged to fit a specific size, maintaining the same shape.

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 are the dimensions of a similar rectangle with a scale factor of 2?

Back

The dimensions would be 20 cm (length) and 10 cm (width).

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter (P) of a rectangle is calculated using the formula P = 2(length + width).

Front

If the scale is 1 inch = 5 feet, how many inches represent 20 feet?

Back

4 inches represent 20 feet (20 feet ÷ 5 feet/inch = 4 inches).

Front

What is the relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

How do you set up a proportion to find a missing length in similar figures?

Back

Set up a proportion by equating the ratios of corresponding sides. For example, if triangle A has sides a, b, and c, and triangle B has sides x, y, and z, then a/x = b/y = c/z.

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 building is 32 feet tall (set up the proportion: 12/9 = x/24, solving gives x = 32).

Front

What is the perimeter of a triangle with sides measuring 10 cm, 12 cm, and 14 cm?

Back

The perimeter is 36 cm (10 + 12 + 14 = 36).