Chapter 1 Review

1. Chapter 1 Review Jamie Kim, Claire Jablonski, Jordan Armstrong, Jaylyn Shin, Olivia Hoover

2. 1.1 Points, Lines, and Planes This bullet is a point. A star in the solar system is a point. A pencil tip is a point. Points have no shape or size and is written as point P a pole, a pencil, and an edge of paper are all examples of lines. There is a line through any two points and is written as line n or line AB or AB.

3. Examples of planes in real life are sheets of paper, floor tiles, and ceiling tiles. There is exactly 1 plane between 3 points and it is written as plane T or plane XYZ, YZX, etc. using the names of the three non-collinear points.

4. 1.2 Linear Measure and Precision XY PQ XY PQ What is the notation for a line segment? Segment lengths are _________. Segments are ____________.

5. 1.3 Distances and Midpoints a + b 2 ( ) X1+ X2 Y1 + Y2 2 , 2 ------------------------------------------------------------------------------------------------------------------------------------------------------ A Segment Bisector is a segment, line, or plane that intersects a segment at its midpoint. To find the midpoint on… A number line: ____ a and b being the endpoints of the segment. A coordinate plane : (x1, X2) and (Y1, Y2) being the coordinates of the endpoints of the segment

6. Finding the midpoint on a coordinate plane. • Set up the formula by substituting the x coordinates of the two endpoints where it says X2 and X1. • Do the same for the y coordinates and Y2 and Y1. • Solve the equation. ( ) X1 + X2 Y1 + Y2 2 , 2

7. To find the distance on a number line, AB = I b – a I or I a – b I a and b being the endpoints of the segment. To find the distance between two points on a coordinate plane use either the… Distance Formula: Or Pythagorean Theorem:

8. Pythagoras of Samos born- c. 570 BC in Samos died- c. 495 BC (aged around 75) in Metapontum an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. All of what we know about him comes from what his students wrote, and from this, we know that Pythagoras was a mathematician, philosopher, speaker, teacher, musician, vegetarian, and religious leader who was fascinated by the patterns of mathematics in nature He moved to Croton (a city in southern Italy) and started a religious and philosophical school there The school’s most important discovery was that the side of a square was shorter than the diagonal.(this showed that irrational numbers existed) also studied numbers and their relationships with musical harmonies

9. 1.4 Angle Measures Congruent Angles: Angle Bisector: an interior ray that divides an angle into 2 congruent angles

10. 1.5 Angle Relationships Adjacent Angles Vertical Angles Linear Pair Complementary Angles Supplementary Angles Perpendicular Lines

11. Find x • Find the measure of angle ABC • Set the measure of angle ABC equal to 9x+3 • Solve the equation. A 87˚ 9x+3 B C

12. 1.6 Polygons What is a polygon? Draw an example. Now draw these types of polygons! Convex polygons: Each interior angle is less than180 degrees. Concave polygons: Has an interior angle greater than 180 degrees. Regular polygons: Convex polygon with congruent sides and congruent angles

13. Classifying Polygons Draw it! n-gon: a polygon with n sides 3-gon = 3 sided polygon = =___________. 8-gon = 8 sided polygon = = ___________. 9-gon = 9 sided polygon = =___________.

14. Now for a review game!