1. Session 2
Draw six segments that pass through every dot in the figure without taking your pencil off the paper.

2. Warm-up: Using the Pythagorean Theorem
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2
Pythagorean Theorem
= x2
Substitute 2 for a, 6 for b, and x for c.
40 = x2
Simplify.
Find the positive square root.
Simplify the radical.

3. Warmup #2: Using the Pythagorean Theorem
Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.
a2 + b2 = c2
Pythagorean Theorem
42 + b2 = 122
Substitute 4 for a and 12 for c.
b2 = 128
Multiply and subtract 16 from both sides.
Find the positive square root.

4. Bonus: Using the Pythagorean Theorem
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2
Pythagorean Theorem
(x – 2) = x2
Substitute x – 2 for a, 4 for b, and x for c.
x2 – 4x = x2
Multiply.
–4x + 20 = 0
Combine like terms.
20 = 4x
Add 4x to both sides.
5 = x
Divide both sides by 4.

5. Homework Review
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

6. Geometry Vocabulary
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

7. Point An exact position or location in a given plane.
Point A or Point B

8. Line
The set of points between points A and B in a plane and the infinite number of points that continue beyond the points.
Written as

9. Line Segment
A line with two endpoints.
Written as

10. Ray A line that starts at A, goes through B, and continues on.
Written as

11. Plane
A flat, two-dimensional surface that extends infinitely far.

12. Angle Formed by 2 rays coming together at a common point (Vertex)
The angle is

13. Right Angle
An angle that measures 90°.

14. Acute Angle
An angle measuring less than 90° but greater than 0°.

15. Obtuse Angle
An angle measuring greater than 90° but less than 180°.

16. Parallel Line
Lines in a plane that either do not share any points and never intersect, or share all points.
Written as

17. Perpendicular Line Two lines that intersect at a right angle (90°).
Written as

18. Circle
The set of points on a plane at a certain distance, or radius, from a single point, the center

19. Distance along a line
The linear distance between two points on a given line.

20. How far apart are the points on the line segment?

21. How far apart are the points on the line segment?
Hmmm…

22. CW Vocabulary Practice WS

23. Angle Addition Postulate
If B lies on the interior of ÐAOC,
then mÐAOB + mÐBOC = mÐAOC. B A
mÐAOC = 115°
50°
65° C O

24. A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114.
Example 1:
Example 2: G
114° K
46°
95°
19° H
This is a special example, because the two adjacent angles together create a straight angle.
Predict what mÐABD + mÐDBC equals.
ÐABC is a straight angle, therefore mÐABC = 180.
mÐABD + mÐDBC = mÐABC
mÐABD + mÐDBC = 180
So, if mÐABD = 134,
then mÐDBC = ______ J
Given: mÐGHK = 95
mÐGHJ = 114.
Find: mÐKHJ.
The Angle Addition Postulate tells us:
mÐGHK + mÐKHJ = mÐGHJ
95 + mÐKHJ = 114
mÐKHJ = 19.
Plug in what you know. 46
Solve.

25. Set up an equation using the Angle Addition Postulate.
Given:
mÐRSV = x + 5
mÐVST = 3x - 9
mÐRST = 68
Find x.
Algebra Connection R V
Extension: Now that you know x = 18, find mÐRSV and mÐVST.
mÐRSV = x + 5
mÐRSV = = 23
mÐVST = 3x - 9
mÐVST = 3(18) – 9 = 45
Check:
mÐRSV + mÐVST = mÐRST
= 68 S T
Set up an equation using the Angle Addition Postulate.
mÐRSV + mÐVST = mÐRST
x x – 9 = 68
4x- 4 = 68
4x = 72
x = 18
Plug in what you know.
Solve.

26. x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 C B
mÐBQC = x – 7 mÐCQD = 2x – 1 mÐBQD = 2x + 34
Find x, mÐBQC, mÐCQD, mÐBQD. C B
mÐBQC = x – 7
mÐBQC = 42 – 7 = 35
mÐCQD = 2x – 1
mÐCQD = 2(42) – 1 = 83
mÐBQD = 2x + 34
mÐBQD = 2(42) + 34 = 118
Check:
mÐBQC + mÐCQD = mÐBQD
= 118 Q D
mÐBQC + mÐCQD = mÐBQD
x – 7 + 2x – 1 = 2x + 34
3x – 8 = 2x + 34
x – 8 = 34
x = 42
x = 42
mÐBQC = 35
mÐCQD = 83
mÐBQD = 118
Algebra Connection
Slide 5

27. HW Angle Addition Postulate WS