Unit 6 - Dilations

Question 1

What is the equation for the scale factor?

Answer 1

r = measure of image/ measure of preimage

Question 2

What results in the enlargement and reduction of the pre - image?

Answer 2

Enlargement: r > 1
Reduction: 0 < r < 1

Question 3

How to determine size of preimage & image of tri. on coordinate plane?

Answer 3

Measure the size of the base

Question 4

How can you find the measure of the image by using a scale factor?

Answer 4

Multiply “r” by the preimage

Question 5

How do you perform a dilation on the coordinate plane?

Answer 5

(rx, ry)

Question 5

What are the two properties of Dilations? (2)

Answer 5

1. Corresponding sides are in proportion
2. Corresponding angles are congruent

Question 6

How do you determine that the image is a dilation of the image? (3)

Answer 6

1. Find SF (Image/Preimage)
2. Plug in 2 diff. sides of both triangles
3. If SF matches up, it’s a Dilation

Question 7

What is notation for Scale Factor?

Answer 7

r for “ratio”

Question 8

On a coordinate plane, what do corresponding preimage and image points have in common with the origin?

Answer 8

They are collinear with the center of dilation (typically the origin)

Question 9

What happens to the images in relationship to the center of dilation when it shrinks or enlarges? (2)

Answer 9

Shrinks - Closer to the COD
Enlarges - Farther from the COD

Question 9

True or False:
Corresponding Parts of a preimage and image in a dilation are parallel to each other

Answer 9

True

Question 10

How can you find the center of Dilation when only given A & B from the preimage and A’ & B’ from the image? (2)

Answer 10

1. Draw 2 lines thru corr. points
2. Intersection is the COD

Question 10

How do you create a dilation of a figure with a SF less than 1?

Answer 10

Perpendicular Bisector

Question 11

How do you create a dilation of a figure with a SF greater than 1? (3)

Answer 11

1. Extend the Side
2. Copy distance from COD to pre - point
3. Copy once for 2, twice for 3, etc.

Question 12

How can you CONSTRUCT a dilation when only given the preimage and one side?

Answer 12

Copy the Angle

Question 13

What is the Triangle Side Splitter Theorem? (4)

Answer 13

1. If a line inside a triangle
2. Is parallel to one side of the triangle
3. It splits the other two sides
4. Into proportionally equal segments

Ex: In triangle 𝐴𝐵𝐶, a line 𝐷𝐸 is drawn parallel to side 𝐵𝐶. The line 𝐷𝐸 intersects 𝐴𝐵 at point 𝐷 and 𝐴𝐶 at point 𝐸.

AD/DE = AE/EC

Question 14

What is the “Proportional Parts of Parallel Lines”? (4)

Answer 14

1. 3 or more parallel lines
2. Are cut by two transversals
3. Divide transversals
4. Into proportionally equal segments

If three parallel lines intersect two transversals, and the segments formed on the first transversal are 4 units and 6 units, and a segment on the second transversal is 8 units, the corresponding segment on the second transversal will be 12 units.

Question 15

Definition of Midsegment (3)

Answer 15

1. A segment
2. Endpoints are midpt. of two side of tri.
3. Every tri. has 3 mid segments

Question 16

Definition of Triangle Midsegment Theorem (2)

Answer 16

1. Midseg. parallel to one side of a triangle
2. Midsegment = 1/2 of that side