I am a rigid motion that turns a figure based on a number of degrees and direction.
Rotation
Complete the following sentence about triangles.
If one triangle can be mapped to another triangle by a series of rigid transformations, then the triangles are called _________ and the corresponding ______ and angles are congruent.
congruent; sides
A. (30, -6)
True or False: I undergo a translation and a reflection. My corresponding side lengths are preserved.
True
I’m the rare case when today comes before yesterday. What am I?
A dictionary
I usually let my nonrigid transformation know how much bigger or smaller to make the image.
Scale Factor
Triangle U
We can use only rigid motions to get from the green (R) to the purple (U) triangle. We can do this many different ways. One way would be to do a 180 degree rotation and translate right and down.
D. 3
True or False: After a rotation and a dilation, my area is preserved.
False
If a mile is 5280 feet, how many feet are in 1/4 of a mile
1320 feet
After a transformation, if I keep all of the same angle measures, perimeter, or area we say that these properties are _________ .
Preserved
A series of transformations were applied to triangle JKL to create triangle XYZ.
If triangle JKL and triangle XYZ are congruent, which of the following transformations could have been applied to triangle JKL?
I. reflection II. rotation III. translation IV. dilation
C. I, II, and III only
(reflection, rotation, translation)
1) What is the area of triangle QRS?
2) What is the area of the image, triangle Q'R'S' after a dilation with a scale factor of 5?
1) 10
2) 50
True or False: After a reflection and a dilation, my corresponding angles are preserved.
True
If a rooster lays an egg on the exact peak of a barn, which side does it fall?
A rooster does not lay eggs.
I am the type of transformation consisting of only rigid motions that preserves all angle measures, side lengths, area, and perimeter.
Congruence
Yes, the two figures are congruent since two rigid transformations (rotation and translations) will map one figure to another. All corresponding side lengths/angle measures, and perimeter/area are preserved.
1) What is the perimeter of triangle QRS (round to the nearest tenth)?
2) What is the perimeter of the image, triangle Q'R'S', after a dilation with a scale factor of 3?
1) 15.4
2) 46.2
Compare and contrast congruence and similarity transformations.
Both types of transformations change the figure in some way. This could be turning, flipping, sliding, or changing the size of the figure. These are different because similarity transformations will not always preserve measurements (side lengths, perimeter, area), but congruence transformations keep all of these equal.
I am two consecutive odd numbers. My sum is 76. What two numbers am I?
37, 39
I do not preserve side lengths, area, and perimeter. But, my corresponding angle measures are always preserved.
Similarity
90 degree CCW rotation about point N and a translation 7 units to the right
Triangle XYZ and triangle X'Y'Z' are given on the coordinate plane below.
List a sequence of transformations that shows that triangle XYZ is similar to triangle X'Y'Z'?
90 degree clockwise rotation and a dilation with a scale factor of 1.5.
Explain why a dilation preserves corresponding angle measures, but not its perimeter.
A dilation is a nonrigid motion, which will produce the same shape and a different size. Since the shapes will be identical, the angle measures are preserved. Since a dilation will make a figure bigger or smaller, the perimeter of the preimage and image will not be the same.
A cowboy rides into town on Friday. He stays three days, then rides out of town on Friday. How?
The horse's name was Friday.