Similar Figures

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 the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

If two figures are similar, what can be said about their angles?

Back

If two figures are similar, all corresponding angles are equal.

Front

If a triangle has sides of lengths 3, 4, and 5, what are the lengths of the sides of a similar triangle with a scale factor of 2?

Back

The lengths of the sides of the similar triangle would be 6, 8, and 10.

Front

How do you find the height of a similar figure if you know the height of another figure and their shadow lengths?

Back

Use the proportion of the heights to the lengths of their shadows. If height1/shadow1 = height2/shadow2, you can solve for the unknown height.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the scale factor.

Front

If a rectangle has a length of 4 cm and a width of 2 cm, what are the dimensions of a similar rectangle with a scale factor of 3?

Back

The dimensions of the similar rectangle would be 12 cm (length) and 6 cm (width).

Front

How do you determine if two figures are similar?

Back

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

Front

What is the formula to find the missing side of similar triangles?

Back

If triangle A has sides a, b, c and triangle B has sides x, y, z, then a/x = b/y = c/z.

Front

If a 10 ft tall tree casts a 15 ft shadow, how tall is a statue that casts a 30 ft shadow?

Back

The statue is 20 ft tall.