Unit 2 - Transformations, Rigid Motions, and Congruence

Question 1

Transformation

Answer 1

moving it from one point to another

(x,y) –> (x+h,y+k)

Question 2

Dilations

Answer 2

change in size

if there’s multiplication or division it’s DILATION

Scale Factor {k= image/preimage}
(a,b) –> (ka, kb)

Question 3

Rigid Motions / Isometries

Answer 3

transformations that preserve shape and size

Question 4

Rotations

Answer 4

when a point is rotated by an angle around another point by constructing a segment

Counterclockwise:
- 90 - (a,b) –> (-b,a)
- 180 - (a,b) –> (-a, -b)
- 270 - (a,b) –> (b,-a)

Clockwise:
- 90 - (a,b) –> (b, -a)
- 180 - (a,b) –> (-a,-b)
- 270 - (a,b) –> (-b, a)

Question 5

Properties of Rigid Motions

Answer 5

1. Rigid motions transform lines into lines, segments into segments, and rays into rays.
2. Rigid motions preserve the distance between points and the length of line segments
3. Rigid motions preserve angles between lines, rays, and segments

OR

1. All rigid motions map lines to lines, segments into segments, and rays into rays.
2. All rigid motions preserve distance and angle measurements.
3. Rotation of a line 180 degrees about a point not on the line produces a parallel line
4. Rotation of a line 180 degrees about a point that does lie on the line produces the same line.
5. Translation of a line not along the line produces a parallel line.
6. When a point is reflected across a line, the segments connecting the point and its image is perpendicularly bisected by the line

Question 6

A line that is rotated 180 about a point NOT on the line will ALWAYS result in a line parallel to the original

Question 7

Reflections

Answer 7

x-axis: (a,b) –> (a,-b)
y-axis: (a,b) –> (-a,b)
y = x: (a,b) –> (b,a)
y = -x: (a,b) –> (-b,-a)

Question 8

Isosceles Triangles

Answer 8

has at least two sides with equal lengths (legs)

Question 9

All of a triangles equal 180 degrees

Question 10

Transformation Properties

Answer 10

1. map lines to parallel lines
2. preserve angles
3. preserve length/ distance

Question 11

Congruence

Answer 11

if a sequence of rigid motions is found that makes the two figures lie exactly on top of each other then the two figures are congruent

Question 12

Triangle Congruence

Answer 12

two triangles are congruent if a sequence of rigid motions can make the vertices coincide with the other triangles

Question 13

Symmetries

Answer 13

a transformation that maps a figure onto itself is known as the symmetry of the figure

Question 14

Regular Polygons

Answer 14

a polygon whose sides are all equal in length and angles are all equal