Show:
Dilation
Similar Figures
Similar Triangles
Using proportions
Solve it
100
These determine the position and the size of the image of a figure after the dilation, respectively

Center of dilation and Scale factor

100

4 kinds of similarity transformations

reflections, translations, rotations and dilations

100
In similar triangles, are there any measurements that remain the same?
Corresponding angles are congruent


100

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)

100

The geometric mean of 9 and 25

15

200
These are the input and output of a dilation, transformed by the scale of dilation
pre image and image
200
What is something true about all circles

All circles are similar

200

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)

200

How many similar triangles do you create when drawing the altitude of a right triangle to its hypotenuse? 

3
200

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

300
Dilations preserve these

angle measure, betweenness, collinearity, orientation

300

two plane figures are similar if and only if

one figure can be mapped to the other through one or more similarity transformations

300

All triangle similarity theorems

AA

SSS (proportionality)

SAS


300
What is A:B in ratios?

A / (A+B)

300

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)

400

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. 

400

How can you write transformations in coordinate form?

(translations and dilations)

(x,y)->(x+a, y-b) (translation)

(x,y)->(kx,ky) (dilation)

400

If a triangle ABC is similar to triangle XYZ and YZX, what special kind of triangle is ABC?

Equilateral triangle

400

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.

400

Describe a similarity transformation that maps trapezoid PQRS to trapezoid WXYZ

Reflection in the y axis and 

(x, y) → ( x/3,y/3)