Dilation
Center of dilation and Scale factor
4 kinds of similarity transformations
reflections, translations, rotations and dilations
What theorem can we apply when we know there's a parallel line to the base of a triangle cutting through it?
Triangle proportionality theorem (it relates not only the sides of the triangle, but the segments created by the cut of the parallel line)
The geometric mean of 9 and 25
15
All circles are similar
Can you say two triangles are similar just by knowing two things about each? If yes, which two things?
Yes, if two pairs of angles are congruent, then the triangles are similar. (AA theorem)
How many similar triangles do you create when drawing the altitude of a right triangle to its hypotenuse?
Suppose you are given right triangle ABC with its non right angles be 30 and 60, and another right triangle DEF, what one piece of information do we need to say that these are similar triangles
That either of the non right angles in DEF is either 30 or 60
angle measure, betweenness, collinearity, orientation
two plane figures are similar if and only if
one figure can be mapped to the other through one or more similarity transformations
All triangle similarity theorems
AA
SSS (proportionality)
SAS
A / (A+B)
Find the center of dilation of two squares, with A(-4,4), B(-4,-4), C(4,-4), D(4,4) and A'(8,1), B'(8,-1), C'(10,-1), D'(10,1)
k=1/4
center of dilation (12,0)
How can we determine the scale of dilation just from the coordinates of a figure?
If the dilation is center on the origin, then the dilation goes (x,y)->(kx,ky) where k is the dilation factor.
How can you write transformations in coordinate form?
(translations and dilations)
(x,y)->(x+a, y-b) (translation)
(x,y)->(kx,ky) (dilation)
If a triangle ABC is similar to triangle XYZ and YZX, what special kind of triangle is ABC?
Equilateral triangle
What does the converse of the proportionality theorem states?
If a line divides tow sides of a triangle proportionally, then it is parallel to the third side.
Describe a similarity transformation that maps trapezoid PQRS to trapezoid WXYZ
Reflection in the y axis and
(x, y) → ( x/3,y/3)