DILATIONS
What is a dilation?
A transformation that changes size but not shape
What is the scale factor?
The number used to multiply coordinates in a dilation
What is the coordinate rule for dilation?
(x, y) → (kx, ky)
What does similar mean?
Figures with same shape, different size
what two initals refers to Angle‑Angle similarity?
AA
What is enlargement
A scale factor greater than 1
What is an isometry?
A distance-preserving transformation between metric spaces
Solve X(2,-1), G(4,4), W(4,-1) k=0.25
X'(0,5 , -0.25) G'=(1,1) W'=(1,-0.25)
What does congruent mean?
Angles that are in similar figures
What is AA similarity?
Two angles guarantee triangle similarity
What is a reduction?
A scale factor between 0 and 1
What is a reduction?
Rewriting an expression into a simpler form.
Solve I(-1,0),M(-1,1),B(1,5) k=4.5
B'=(4,5 , 20,5)
What does proportional mean?
Word that describes corresponding sides
What is SSS similarity?
All sides proportional proves this
Is 0.6 Reduction, Enlargement, or isometry
reduction
What is the scale factor?
The ratio of corresponding side lengths or a number that tells how much a figure is enlarged or reduced during a dilation.
True or False:Coordinates always increase False
On a number line or coordinate plane, values can increase or decrease.
Two polygons have all corresponding angles congruent and all corresponding side lengths proportional. What is the geometric term used to describe their relationship.
Similar figures
What is SAS similarity?
Two sides proportional + included angle
What is the center of dilation?
The point from which a dilation is performed
A rectangle has side lengths of 4 cm and 6 cm. A similar rectangle is created using a scale factor of 2. What are the side lengths of the new rectangle.
8 cm and 12 cm
A triangle with vertices at A(2, 1), B(4, 3), and C(6, 1) is dilated from the origin by a scale factor of 3. What are the coordinates of point A after the dilation.
(6, 3)
If a triangle has a scale factor of 3 each corresponding side length in the larger triangle is how many times longer than the original.
3 times
Two triangles have two pairs of proportional sides and the included angle between those sides is congruent. What is the similarity postulate used to prove the triangles are similar.
SAS (Side–Angle–Side)