Topic 7: Dilations and Similarity II

Front

What does it mean for two shapes to be similar?

Back

Two shapes are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is a scale factor in dilations?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a shape. It determines how much larger or smaller the dilated image will be compared to the original shape.

Front

If the scale factor is 2, what happens to the dimensions of a shape?

Back

If the scale factor is 2, the dimensions of the shape will double. For example, a shape with dimensions 3 units by 4 units will become 6 units by 8 units.

Front

What is the algebraic rule for a dilation with a scale factor of 0.5?

Back

The algebraic rule for a dilation with a scale factor of 0.5 is (x, y) --> (0.5x, 0.5y). This means each coordinate is multiplied by 0.5.

Front

How do you find the corresponding angle in similar triangles?

Back

To find the corresponding angle in similar triangles, look for the angle that is in the same position relative to the other angles in both triangles.

Front

What is the relationship between the sides of similar figures?

Back

The lengths of corresponding sides of similar figures are proportional. This means that the ratio of the lengths of any two corresponding sides is the same.

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 8 cm, what is the scale factor?

Back

The scale factor is 2, because DE (8 cm) is twice the length of AB (4 cm).

Front

What is the formula to calculate the area of a dilated shape?

Back

The area of a dilated shape can be calculated using the formula: Area of original shape × (scale factor)².

Front

If a shape is dilated by a scale factor of 3, how does its area change?

Back

If a shape is dilated by a scale factor of 3, its area increases by a factor of 3², which is 9 times the original area.

Front

What is a corresponding side in similar figures?

Back

A corresponding side in similar figures is a side that is in the same relative position in both shapes.