Dilation and Similarity Concepts

Miss Rodriguez introduces a lesson on similarity and dilation, focusing on understanding the concept of similar shapes and the transformation called dilation. The lesson includes an exploratory challenge to identify similar shapes, a discussion on proportions using image resizing, and a detailed explanation of dilation. Examples of scale factors and their effects on shapes are provided, followed by exercises to reinforce the concepts learned.

What is the main difference between similar and congruent figures?

• Similar figures have the same shape but not necessarily the same size.

• Congruent figures have different shapes and sizes.

• Similar figures have the same size but different shapes.

• Congruent figures have the same shape but different sizes.

In the exploratory challenge, which pair of shapes was identified as similar?

• Two congruent pentagons.

• Two smiley faces with different proportions.

• Two triangles of different sizes.

• Two quadrilaterals, one rectangle and one square.

What does the term 'dilation' mean in mathematics?

• To change the color of a shape.

• To enlarge or shrink a shape proportionally.

• To rotate a shape around a point.

• To reflect a shape across a line.

Which of the following is needed for a dilation transformation?

• A degree of rotation.

• A line of reflection.

• A center of dilation and a scale factor.

• A vector for translation.

If a rectangle is dilated by a scale factor of 2, what happens to its dimensions?

• The dimensions are doubled.

• The dimensions remain the same.

• The dimensions are tripled.

• The dimensions are halved.

How do you calculate the new length of a side after dilation?

• Add the scale factor to the original length.

• Multiply the original length by the scale factor.

• Divide the original length by the scale factor.

• Subtract the scale factor from the original length.

What happens to a shape if the scale factor is less than 1 but greater than 0?

• The shape becomes larger.

• The shape becomes smaller.

• The shape changes color.

• The shape remains the same size.

If the original length of a segment is 5 inches and the scale factor is 4, what is the new length?

• 9 inches

• 15 inches

• 20 inches

• 25 inches

What is the scale factor if the original length is 3 cm and the dilated length is 9 cm?

• 1

• 2

• 3

• 4

What should you remember about the scale factor in dilation?

• It is always greater than 1.

• It has units like cm or inches.

• It is a multiplier without units.

• It is always less than 1.