Dilations
Similarity
Slope
Final Jeopardy
100
True or False:
Dilations of an angle are not congruent to the original angle.
False
100
Triangle A has a 62 degree angle and a 35 degree angle. Triangle B has an 83 degree angle and a 62 degree angle. Are they similar?
Yes, triangle A and B are similar.
100
True or False:
If triangles ABC and ADE are slope triangles for a line, then we know they are similar triangles.
True
100
Which of the following polygons B, C, D, and E are similar to polygon A?
Polygons B and D are similar to polygon A.
200
Plot the image of point C under a dilation about center P with a scale factor of 3.
200
Explain how you know these two figures are similar.
These two figures are similar because their corresponding side lengths either increase or decrease by the same scale factor and their corresponding angles are congruent. The two figures can also be described as a transformation involving both a translation and rotation.
200
Write an equation for the slope of the line.
y/x=5/3
300
Lin drew a triangle and a dilation of the triangle with scale factor of 1/2. Which triangle is the dilation? Explain how you know.
Triangle AED is the dilation because there is a scale factor of 1/2, so we know a reduction has occurred. The original image has been made smaller.
300
Triangle ABC and some of its measurements are shown. Triangle XYZ, not shown, is similar to triangle ABC. What is the measure, in degrees, of angle Z?
Angle Z= 45 degrees
300
Find the slope of the line that passes through both points in simplest form.
(0,-1) and (2,3)
Slope = 2
400
The smaller triangle is dilated to create the larger triangle. The center of dilation (3,0). What is the scale factor?
Scale factor = 3
400
These two triangles are similar. Find side lengths a and b.
a=7
b=15
400
Is the point (20, 13) on this line? Explain your reasoning.
Yes. The slope of the line is 1/2. We see there is a point (0,3) on the line. If we calculate the change in y divided by the change in x using this point, we would get 10/20 which simplifies to 1/2.
500
Determine the scale factor and missing side length for the following pair of dilated figures. The figure on the left is the pre-image and the figure on the right is the image.
Scale factor= 5
h= 5 inches
500
Triangles ABC, EFD, and GHI are all similar. The side lengths of the triangles all have the same units. Find the unknown side lengths.
c=2
d=10
e=10
h= 12/5
500
Find the value of a.
a=2