Exploring Dilations and Similarity in Geometry

In this lesson, Miss DB covers chapter 7, section 6, focusing on dilations and similarity in the coordinate plane. The lesson explains the concept of dilations, including how scale factors affect the size of figures while maintaining their shape. Examples are provided to illustrate enlargements and reductions. The use of Sketchpad is demonstrated to plot points and prove the similarity of triangles using methods like side-side-side and side-angle-side. The lesson emphasizes the application of similarity properties and coordinate proofs.

What is a dilation in the context of transformations?

• A transformation that changes the shape of a figure.

• A transformation that reflects a figure.

• A transformation that rotates a figure.

• A transformation that changes the size of a figure but not its shape.

What does a scale factor greater than 1 indicate in a dilation?

• A reduction

• An enlargement

• A reflection

• A translation

If a triangle is dilated by a scale factor of 0.5, what happens to the triangle?

• It rotates.

• It reflects.

• It becomes smaller.

• It becomes larger.

In the example of dilating a rectangle by a scale factor of 5/2, what is the new coordinate of point B if the original coordinate is (0, 4)?

• (0, 6)

• (0, 10)

• (0, 12)

• (0, 8)

What tool can be used in Word to draw lines for plotting points?

• Insert -> Picture

• Insert -> Table

• Insert -> Chart

• Insert -> Shapes -> Line

How do you find the image of a point after a dilation with a scale factor of K?

• Divide each coordinate by K.

• Multiply each coordinate by K.

• Subtract K from each coordinate.

• Add K to each coordinate.

Given that triangle TUV is similar to triangle RST, how do you find the scale factor?

• By adding the lengths of corresponding sides.

• By multiplying the lengths of corresponding sides.

• By subtracting the lengths of corresponding sides.

• By dividing the lengths of corresponding sides.

What is the coordinate of point U if the scale factor is 3/4 and the original coordinate is (0, 16)?

• (0, 8)

• (0, 12)

• (0, 4)

• (0, 10)

Which method can be used to prove that two triangles are similar?

• SAS

• All of the above

• SSS

• AAA

What is the benefit of using Sketchpad for proving triangle similarity?

• It provides a visual representation.

• It allows for easy manipulation of figures.

• It automatically calculates distances.

• All of the above