1. REVIEW OF LAST WEEK

2. To transform something is to change it
To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include:
Translation
Rotation
Reflection
Dilation

3. A “slides” an object a fixed distance in a given direction
A “slides” an object a fixed distance in a given direction. The original object and its translation have the, and they
Translations are
Translation
same shape and size
face in the same direction
SLIDES.

4. A is a transformation that turns a figure about a fixed point called the center of rotation.  An object and its rotation are the , but the
rotation
same shape and size
figures may be turned in different directions

5. The line (where a mirror may be placed) is called the line of reflection.  The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection.
A reflection can be thought of as a "flipping" of an object over the line of reflection.
line of reflection
                             
   
                           
If you folded the two shapes together line of reflection the two shapes would overlap exactly!
line of
reflection

6. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
A dilation used to create an image larger than the original is called an enlargement.  A dilation used to create an image smaller than the original is called a reduction.
dilation
same shape
different size.
larger
enlargement
smaller
reduction

8. Acute Angles
An acute angle is an angle measuring between 0 and 90 degrees.
The following angles are all acute angles.

9. Obtuse Angles
An obtuse angle is an angle measuring between 90 and 180 degrees.
The following angles are all obtuse.

10. Right Angles A right angle is an angle measuring 90 degrees.
The following angles are both right angles.

11. Straight Angle
A straight angle is 180 degrees.

12. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

13. Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

14. Example 1 Find the value of x by making an equation.
This is on p. 16 of the Study Guide problem #2.

15. Example 2 Find the value of x by writing your equation.
This is on p. 16 of the Study Guide problem #3.

16. Example 3 Find the value of x.
This is on p. 16 of the Study Guide problem #1.

17. Example 4 Find the value of x.
This is on p. 16 of the Study Guide problem #6.

18. Example 5 Find the value of x.
This is on p. 16 of the Study Guide problem #3.

19. Do work sheet #1-16

20. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 2 are called SUPLEMENTARY ANGLES
They are a linear pair. ALL linear pairs are supplementary (their measures add up to 180̊ ).
Name other supplementary pairs:

21. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 3 are called VERTICAL ANGLES
They are congruent m<1 = m<3
Name other vertical pairs:

22. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 1 and < 5 are called CORRESPONDING ANGLES
They are congruent m<1 = m<5
Corresponding angles occupy the same position on the top and bottom parallel lines. Name other corresponding pairs:

23. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 4 and < 6 are called ALTERNATE INTERIOR ANGLES
They are congruent m<4 = m<6
Alternate Interior on the inside of the two parallel lines and on opposite sides of the transversal. Name other alternate interior angles.

24. Parallel lines cut by a transversal2 1 3 4 6 5 7 8
< 4 and < 6 are called ALTERNATE EXTERIOR ANGLES
They are congruent m<2 = m<8
Alternate Interior on the inside of the two parallel lines and on opposite sides of the transversal. Name other alternate exterior angles.

25. TRY IT OUT 2 1 3 4 6 5 7 8
The m < 6 is degrees, Find the rest of the angles.

26. TRY IT OUT 2x + 20 x + 10 What do you know about the angles?
Write the equation.
Solve for x.
SUPPLEMENTARY
2x x + 10 = 180
3x + 30 = 180
3x = 150
x = 30

27. TRY IT OUT 3x - 120 2x - 60 What do you know about the angles?
Write the equation.
Solve for x.
ALTERNATE INTERIOR
3x = 2x - 60
x =
Subtract 2x from both sides
Add 120 to both sides