Exploring Dilations and Similarity in Geometry

This lesson covers dilations and similarity in geometry. It explains how to perform dilations, identify the center of dilation, and use scale factors to enlarge or reduce shapes. The lesson also discusses how to determine if figures are similar by checking if they are dilations of each other with the same scale factor. Examples are provided to illustrate these concepts, and students are guided on how to calculate unknown side lengths of similar figures.

What is the main objective of this lesson?

• To draw complex geometric figures

• To calculate the area of shapes

• To understand dilations and similarity

• To learn about rigid transformations

What is a dilation in geometry?

• A transformation that changes the shape

• A transformation that rotates the shape

• A transformation that changes the size

• A transformation that reflects the shape

What do you need to know to perform a dilation?

• The angle of rotation

• The center of dilation and the scale factor

• The translation vector

• The line of reflection

If a shape is dilated with a scale factor of 2, what happens to the distances from the center of dilation?

• They are tripled

• They are doubled

• They are halved

• They remain the same

When the center of dilation is outside the shape, where will the dilated shape be?

• Inside the original shape

• On top of the original shape

• It depends on the scale factor

• Outside the original shape

What does it mean for two figures to be similar?

• They have the same area

• They have the same shape but different sizes

• They have the same size but different shapes

• They have the same perimeter

How can you determine if two shapes are similar?

• By checking if they have the same angles

• By checking if they have the same area

• By checking if they are dilations of each other with the same scale factor

• By checking if they have the same side lengths

If a side of a small trapezoid is 9 units and the corresponding side of a larger trapezoid is 18 units, what is the scale factor?

• 1/3

• 1/2

• 2

• 3

What is the missing side length if a shape is dilated by a scale factor of 5 and the original side length is 1 unit?

• 1 unit

• 25 units

• 10 units

• 5 units

What happens to a shape when it is dilated with a scale factor between 0 and 1?

• It becomes larger

• It becomes smaller

• It rotates

• It reflects