Flashcard: Ratios, Proportions, Similar Figures Geometry

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, expressed as 'a/b = c/d'.

Front

How do you solve for a variable in a proportion?

Back

Cross-multiply the ratios and solve for the variable. For example, if a/b = c/d, then ad = bc.

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

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 corresponding side of the other figure.

Front

If two triangles are similar, what can you say about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

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

Back

The ratio of their areas is the square of the ratio of their sides, so (2:3)² = 4:9.

Front

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

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross products are equal.

Front

What is the relationship between the sides of similar polygons?

Back

The corresponding sides of similar polygons are in proportion.