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 when centered at the origin?

Answer 5

(rx, ry)

Question 6

What are the two properties of Dilations? (2)

Answer 6

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

Question 7

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

Answer 7

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

Question 8

What is notation for Scale Factor?

Answer 8

r for “ratio”

Question 9

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

Answer 9

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

Question 10

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

Answer 10

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

Question 11

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

Answer 11

True

Question 12

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

Answer 12

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

Question 13

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

Answer 13

Perpendicular Bisector

Question 14

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

Answer 14

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

Question 15

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

Answer 15

Copy the Angle

Question 16

What is the Triangle Side Splitter Theorem? (4)

Answer 16

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 17

Using the Triangle Side Splitter Thereom, which sides are proportional in the typical diagram? (2/2)

Answer 17

1. Sides from the same small triangle
2. Is proportional to the extension sides
3. Sides of the Big Tringle
4. Is proportional to the sides of the small triangle

Question 18

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

Answer 18

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 19

Definition of Midsegment (3)

Answer 19

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

Question 20

Definition of Triangle Midsegment Theorem (2)

Answer 20

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