7.5A & 7.5C Proportionality & Similar Figures Knowledge Check

Front

What is proportionality?

Back

Proportionality refers to the relationship between two quantities where their ratio remains constant. For example, if one quantity doubles, the other quantity also doubles.

Front

Define 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 space that is proportionally reduced or enlarged. The scale indicates the ratio of the drawing's dimensions to the actual dimensions.

Front

If a scale drawing has a scale of 1 in = 6 ft, how many feet does 2 inches represent?

Back

2 inches represents 12 feet (2 in x 6 ft/in = 12 ft).

Front

How do you find the actual distance using a map scale?

Back

To find the actual distance, multiply the distance on the map by the scale factor. For example, if the map scale is 1 cm = 20 km and the distance on the map is 3.5 cm, the actual distance is 3.5 cm x 20 km/cm = 70 km.

Front

What is the relationship between corresponding sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal. This means if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.

Front

If triangle RST is similar to triangle RVW and the length of side RS is 6 cm while RV is 12 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2 (6 cm : 12 cm).

Front

What does it mean if two figures are similar?

Back

If two figures are similar, it means they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

How do you determine the scale of a drawing?

Back

To determine the scale of a drawing, compare the dimensions in the drawing to the actual dimensions. For example, if a drawing shows a length of 5 inches and the actual length is 30 feet, the scale is 1 in = 6 ft.

Front

What is the formula for finding the area of similar figures?

Back

The area of similar figures is proportional to the square of the ratio of their corresponding sides. If the ratio of the sides is a:b, then the ratio of the areas is a²:b².