Unit 6 - Dilations Flashcards
What is the equation for the scale factor?
r = measure of image/ measure of preimage (r = i/p)
What results in the enlargement and reduction of the pre - image?
Enlargement: r > 1
Reduction: 0 < r < 1
How to determine size of preimage & image of tri. on coordinate plane?
Measure the size of the base
How can you find the measure of the image by using a scale factor?
Multiply “r” by the preimage
How do you perform a dilation on the coordinate plane when centered at the origin?
(rx, ry)
What are the two properties of Dilations? (2)
- Corresponding sides are in proportion
- Corresponding angles are congruent
How do you determine that the image is a dilation of the image? (3)
- Find SF (Image/Preimage)
- Plug in 2 diff. sides of both triangles
- If SF matches up, it’s a Dilation
What is notation for Scale Factor?
r for “ratio”
On a coordinate plane, what do corresponding preimage and image points have in common with the COD?
They are collinear with the center of dilation (typically the origin)
What happens to the images in relationship to the center of dilation when it shrinks or enlarges? (2)
Shrinks - Closer to the COD
Enlarges - Farther from the COD
True or False:
Corresponding Parts of Preimage and Image in a Dilation are Parallel
True
How can you find the COD when only given A & B from the preimage and A’ & B’ from the image? (2)
- Draw 2 lines thru corr. points
- Intersection is the COD
How do you construct a dilation of a figure with a SF less than 1?
Perpendicular Bisector
How do you create a dilation of a figure with a SF greater than 1? (3)
- Extend the Side
- Copy distance from COD to pre - point
- Copy once for 2, twice for 3, etc.
How can you CONSTRUCT a dilation when only given the preimage and one side?
Copy the Angle
What is the Triangle Side Splitter Theorem? (4)
- If a line inside a triangle
- Is parallel to one side of the triangle
- It splits the other two sides
- 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
Using the Triangle Side Splitter Thereom, which sides are proportional in the typical diagram? (2/2)
- Sides from the same small triangle
- Is proportional to the extension sides
- Sides of the Big Tringle
- Is proportional to the sides of the small triangle
What is the “Proportional Parts of Parallel Lines”? (4)
- 3 or more parallel lines
- Are cut by two transversals
- Divide transversals
- 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.
Definition of Midsegment (2)
- Segment conn. MP of 2 sides of the triangle
- Every triangle has 3 mid segments
Definition of Triangle Midsegment Theorem (2)
- Midseg. parallel to one side of a triangle
- Midsegment = 1/2 of that side
