3. Similar Figures, Scale Factor, Transformations

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, a quantity. In geometry, it is the ratio of the lengths of two corresponding sides of similar figures.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

Front

What does it mean for angles in similar figures?

Back

In similar figures, corresponding angles are always congruent, meaning they have the same measure.

Front

What does it mean for sides in similar figures?

Back

In similar figures, the lengths of corresponding sides are proportional, meaning the ratios of their lengths are equal.

Front

If the scale factor from ΔDEF to ΔABC is 1/3, what does this imply?

Back

This implies that each side of ΔDEF is one-third the length of the corresponding side in ΔABC.

Front

Can two figures be similar if their angles are congruent but their sides are not proportional?

Back

No, if the angles are congruent but the sides are not proportional, the figures cannot be similar.

Front

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

Back

The area of similar figures is proportional to the square of the scale factor.

Front

If the scale factor is 2, how does this affect the area of the figure?

Back

If the scale factor is 2, the area of the new figure will be 2^2 = 4 times the area of the original figure.

Front

What is the scale factor if the lengths of corresponding sides are 3 cm and 9 cm?

Back

The scale factor is 9 cm / 3 cm = 3.

Front

If two triangles have a scale factor of 1/2, what is the ratio of their areas?

Back

The ratio of their areas is (1/2)^2 = 1/4.