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

6. 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

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

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

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

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

11. Right Angle
An angle that measures 90°.

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

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

14. Parallel Line
Lines in a plane that either do not share any points and never intersect.
Written as

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

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

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

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

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

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

21. 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.

22. 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.

23. 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