Basic Rigid Motions
List the 3 Basic Rigid Motions.
1. Translations
2. Rotations
3. Reflections
What is the angle measure of a straight line?
180 degrees.
When we add the 3 angles from a triangle together, what is the sum every time?
180 degrees
State the Pythagorean Theorem Formula.
a2+b2=c2
When making a rotation, what is the only thing that does not move?
The point of rotation.
List all pairs of vertical angles.
1 and 3.
2 and 4.
5 and 7.
6 and 8.
You are given 2 angle measures inside triangle ABC. <ABC=56 degrees. <CAB=42 degrees. What is the measure of <ACB?
82 degrees
What letter is used to represent the hypotenuse in the Pythagorean Theorem Formula? What letters are used to represent the legs?
1. The hypotenuse = c.
2. The legs = a and b.
What three things are needed to describe a rotation?
1. The direction of rotation (clockwise or counterclockwise)
2. The point of rotation.
3. The degree of rotation (how far something rotates).
List all pairs of alternate interior angles.
4 and 6.
3 and 5.
You are given 2 angle measures in triangle FGH. <FGH=32 degrees. <GHF=67 degrees. What is the measure of their exterior angle?
32+67=99 degrees
The Pythagorean Theorem Formula only works for a certain kind of triangle. What is that kind of triangle?
Right triangle
An image was rotated 90 degrees clockwise around point P. It was then translated along vector AB.
Describe a series of rigid motions that would map the new image back onto the original image.
1. A translation back along vector BA.
2. A 90 degree counterclockwise rotation around point P.
List all pairs of corresponding angles.
1 and 5.
2 and 6.
3 and 7.
4 and 8.
You are given an exterior angle measure for triangle JKL. The exterior angle measure is 127 degrees. You are only given one of its remote interior angle measures: 46 degrees. What is the measure of the other remote interior angle?
127-46=81 degrees
Leg a = 9 cm
Hypotenuse = 15 cm
Leg b = ?
(Your answer must include a label!)
Leg b = 12 cm
An image was reflected across line L, translated along vector CD, then translated again along vector JK.
Describe a series of motions that would map the new image back onto the original image.
1. Translate along vector KJ.
2. Translate along vector DC.
3. Reflect across line L.
How many letters do we use to name an angle?
How do you decide the order of the letters?
1. 3 letters
2. Whatever letter is by the angle we are talking about goes in the middle of the 3 letters.
You are given 2 angles in a triangle. One of the angles is 56 degrees. The other angle is 79 degrees. What is the measure of the 3rd angle?
180-56-79=45 degrees
Leg a = 15 inches
Leg b= 20 inches
Hypotenuse (c) = ?
(Answer must include a label!)
25 inches