Chapter 1 pt. 1 Understanding Points, Lines, & Planes Vocabulary & Practice

Warm – Up: The Coordinate Plane How to plot points on a coordinate plane? How to simplify expressions and solve equations? Warm – Up: The Coordinate Plane 1. ** What is the remainder, if you divide by 7. A. 75  B. 39  2. In a coordinate system, which quadrant is in the lower left-hand portion of the plane? 3. Points N(5, -2) and M(2, -4) lie on the graph of 2x – 3y = 16. Determine whether P(8, 0) is collinear to N and M. 4. Graph three points that lie on the graph of y = 4x – 5. x y

Algebraic Expressions vs. Verbal Expressions How to plot points on a coordinate plane? How to simplify expressions and solve equations? Algebraic Expressions vs. Verbal Expressions Find Your Match Sit beside your match.

Algebra 1 Review Complete “What’s Our Score?” How to simplify expressions and solve equations? What are points, lines, and planes? Algebra 1 Review Complete “What’s Our Score?”

Warm – Up: How to simplify expressions and solve equations? What are points, lines, and planes? Warm – Up: 3. Plot each point. 1. A(0, 0) 2. B(5, 0) 3. C(-5, 0) 4. D(0, 5) 5. E(0, -5) 6. F(-5, -5) 1. Simplify the expression: -y + 3y - 6y + 12y 2. Solve. 4x – 5 + 3x + 36 = 58 x y

Analyze Your Vocabulary Knowledge In groups of 2 or 3, determine if you have any knowledge of each term. *Point Space *Line Coplanar *Plane Collinear *Segments Non-collinear * Pythagorean Theorem Postulate Theorem *Angle Distance *Ray Congruent *Vertex Midpoint *Acute Angle Bisector *Obtuse Angle Proof *Straight Angle Degrees *Adjacent Angle Corollary *Perpendicular lines Linear Pair *Vertical Angles Geometry *Complementary Coordinates *Supplementary Intersection

Pick up: Ruler and Worksheet How to simplify expressions and solve equations? What are points, lines, and planes? Points, Lines, & Planes Pick up: Ruler and Worksheet

Sketch and Investigate Points and Segments Construct two points and label them “A” and “B.” Find the distance between the two points. D = ______ Q1: How can you make the distance between the two points zero?  Draw a segment connecting the two points. Measure the length of the segment.  M = ____ Q2: How does the length of the segment compare to the distance between its endpoints? Construct a second segment CD with endpoint “D” on the first segment. Measure the length of segment CD. M = ____ Q3: How would you find the midpoint of segment CD?   Rays and Lines Draw a ray with endpoint “J” that passes through a point “K.” Note: a ray extends in one direction. Q4: Could ray JK also be called ray KJ? Explain. Q5: Why or Why not can you measure the length of ray JK? Q6: Why can’t you find the midpoint of a ray? Draw point M between point J and Point K. Q7: Give two different names to the ray. R1.__________ R2. ______________  Construct line XY.  Q8: Name two rays and a segment that lie on the line. R1. ________ R2. ________S1.________

(Cont) Sketch and Investigate How to simplify expressions and solve equations? What are points, lines, and planes? (Cont) Sketch and Investigate Q9: List the similarities and differences between segments, rays, and lines. Complete Venn diagram. Ray Segment Fill in Venn diagram with statements below: Finite Infinitely Long Straight Has 0 endpoints Has 1 endpoints Has 2 endpoints Has a midpoint Line

Warm –up: The Real world (chp. 1) Name a real world example of each and draw a picture. A. point B. segment C. ray D. line

Points, Lines, and Planes Points Lines and Planes Video Review terms from video

POINTS a dot Represents a specific location in space Named by one CAPITAL letter Example: ∙A

Lines Infinitely long and straight Has no end points Named by two points on line or one lower case letter Example:

COLLINEAR vs NONCOLLINEAR Collinear: Points that lie on the same line Example: Points M,A, & N are collinear Noncolliear: All points do not lie on the same line Example: Points T, I, & C are noncollinear

RAY SEGMENT Has one end point Extends infinitely in one direction Named by its endpoint and a point that it passes through Example: Ray AB Has two endpoints Part of a line or ray Can be measured Named by its endpoints Example: Segment CD

PLANE Flat surface Extends infinitely in all directions Name by a single CAPITAL letter or by 3 noncollinear points Example : Plane KSX or Plane R X K S

COPLANAR Points that lie in the same plane. Example: Points B, C, D are coplanar Point A, B, C, D are noncoplanar A F B D C

LINES Parallel Lines: Do not intersect; in the same plane Intersecting Lines: Lines that meet at a point Skew Lines: Lines not in the same plane; do not intersect

SPACE A boundless 3-dimensional set of all points

PRACTICE

Practice: How many points name a line? Answer: 2 How many points name a plane ? Answer: 3 noncollinear Draw and label: Line m contains P Answer: on board

Practice: Are points E, F, and C collinear? Answer: yes Are points A, C, D, and E coplanar? Answer: no How many planes appear in this figure? Answer: 5

Practice: Name a point that is not collinear to F and C? Answer: A, B, D, L, or T Identify a point that is not in plane N? Answer: E or F What is the intersection of plane ADE and plane N? Answer: Line AD

Practice: Are points A, L, and T collinear? Answer: no Are points E, F, and T coplanar? Answer: yes Are points B, T, and C collinear?

Draw and label Ray LK Line a and line b intersect at C. line l intersect plane N at X. Points A, B, C, and D are noncollinear. Points A, B, C, and D are noncoplanar.

State whether each best modeled by a point, line, or plane. A star in the sky Answer: point An ice skating rink Answer: plane A telephone wire strung between two poles Answer: line

Individual Practice Homework Open your textbook to page 9. worksheet May work with a partner quietly Complete problems 1-12, 20,21

Warm – Up: Points, Lines, & Planes J H 1. Are points H, J, K, and L coplanar? 2. Name three segments that intersect at X. 3. Are points W, X, Y collinear? 4. What point(s) do plane WXY and segment WH have in common? L K Z W Y X

Quiz: Points, Lines, and Planes No talking during quiz When finish, Pick up a ruler, a marker, and a sheet of patty paper from front table In textbook, read1.6 (p.43) and 1.2 (p.13)

Measuring Segments Distance Midpoint

Measuring Segments Locating the Midpoint of a segment Material: patty paper, ruler, and pencil ***You can locate the midpoint of any segment by using paper folding Draw points A and B anywhere on a sheet of patty paper Connect the points to form segment AB Fold the paper so that the endpoints A and B lie on top of each other. Pinch the paper to make a crease on the segment. Open the paper and label the point where the crease intersects segment AB as C. Point C is the midpoint of segment AB.

YOUR TURN Use a ruler to measure segment AC and segment CB. Repeat the activity with two other segments. Write a sentence to summarize your observation. Video: Midpoint and Distance Groups: Make video tomorrow

Warm-up: Measuring Segments Find a partner Look around, observe your surroundings, and find a “POINT A” and a “POINT B.” Write it down. Measure the distance from “POINT A” to “POINT B,” and find the midpoint.

Return Quiz Any questions

Locate the place that is midway between Conway & Greenville.

Measuring Segments Group Notes &Video Teach Concept Distance Midpoint

Make a video explaining how to find the midpoint and distance given a number line or two coordinates. Resources: Textbook 1.2 p. 13 & 1.6 p.43 and Geometry To Go (bookshelf) The video must include: 1. How to find the midpoint of a specified segment on a number line? Explain. Give example. (25pts) 2. How to find the distance of a specified segment on a number line? Explain. Give example. (25pts) 3. How to find the midpoint of a segment given two coordinates? Explain. Give example. (25pts) 4. How to find the distance of a segment given two coordinates? Explain. Give example. (25pts) 5. Include the following terms correctly in explanations: congruent segments, bisects, and coordinate plane. (bonus)

Measuring Segments -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 T S V Q W R -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 B Measuring Segments P Given: Number Line Two Coordinate Points Midpoint Formula a + b 2 Distance Formula | x2 – x1| Midpoint Formula Distance Formula

Warm-Up How to find the midpoint and distance of a segment? # 1 & 2: True or False, and Explain. 1. The bisector of a segment always intersects the segment at its midpoint. 2. When 2 lines intersect, a plane is formed. #3: Use number line D A C B -4 -3 -2 -1 0 1 2 3 4 3. Find the midpoint and distance of segment AB. 4. Find the distance given (-5, 7) & (8, -10)

Geometry Textbook Online http://my.hrw.com/ Username & Password

View Videos How to find the midpoint and distance given a number line?

T S V Q W R -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 B √Measuring Segments P How to find the midpoint and distance of a segment? Given: Number Line Two Coordinate Points Midpoint Formula a + b 2 Distance Formula | x2 – x1| Midpoint Formula Distance Formula

√ Measuring Segments Points Distance Midpoint How to find the midpoint and distance of a segment? Points Distance Midpoint (-1, 14) And (3, 6) (11, -1) (-3, -7) (6, 5) (0, -1) (-8, 15) (-4, 5) (-4, 1) (-10, -9)

1.2 Measuring Segments and Constructing Segments How to find the midpoint and distance of a segment? 1.2 Measuring Segments and Constructing Segments TWEET On a Post It Note Think About This p. 16

Segment Addition Postulate How to find the midpoint and distance of a segment? Segment Addition Postulate between States: If Q is __________ P and R, then ___________________. Sketch: Examples: Given that B is between A and C, find the missing measure. 1. AB = 6, BC = 4.5, AB_______ PQ + QR = PR

Segment Addition How to find the midpoint and distance of a segment? Example: Given that B is between A and C, find the missing measure. AC = 15, AB = 6, BC _______ Sketch: AB = 2x, BC = 10x, AC= 6, find x.

Practice: Segment Addition How to find the midpoint and distance of a segment? Practice: Segment Addition Statement Draw Solve Given that B is between A and C, find missing measure. AB = 5.3, BC = _?_, and AC = 6.7 AB = 21, BC = 4.3, and AC = _?_. AB = _?_, BC = 18.9, and AC = 23. AB = 6¾ , BC = _?_, and AC = 10. Given that B is between A and C, find the value of x and the measure of BC.   AB = 3x, BC = 5x, and AC = 8.

Warm-Up: Measuring Segments 1. Find the distance and midpoint given A(5, -5) & B(-2, 8). D= M= 2. If B is between endpoints A & C, find each missing measure. A.) If AB = 53 & BC = 21, find AC. B.) If AB= 13 & BC= 2x , find AC = 3x +7. Find x.

Check: Segment Addition How to find the midpoint and distance of a segment? Check: Segment Addition Statement Draw Solve Given that B is between A and C, find missing measure. AB = 5.3, BC = _?_, and AC = 6.7 AB = 21, BC = 4.3, and AC = _?_. AB = _?_, BC = 18.9, and AC = 23. AB = 6¾ , BC = _?_, and AC = 10. Given that B is between A and C, find the value of x and the measure of BC.   AB = 3x, BC = 5x, and AC = 8.

√Check: Segment Addition How to find the midpoint and distance of a segment? √Check: Segment Addition Statement Draw Solve Given that B is between A and C, find the value of x and the measure of BC. AB = 3(x + 7), BC = 2(x – 3), and AC = 50 R is the midpoint of segment ST. Is SR = 3x + 4 and ST = 8x -7, find RT. If XY = ZB, XY = 6x – 8, and ZB = 4x + 6, what is the measure of XY. If J is the midpoint of AB, AJ = 5x + 14, and JB = 3x + 22, what is x and what is AB? Given Find x, if GC = 12x + 4 and CR = 5x + 20. C R G

Quiz: Measuring Segments How to find the midpoint and distance of a segment? Quiz: Measuring Segments No talking during quiz When finish, Complete Segment Addition Crossword (Bonus on Quiz or Test) Complete Chp 1 pt 1 Review

Chapter 1 pt. 1 Review VOCABULARY ANALYZE TRANSFORMATION FIGURES Review each concept for test Use slips as a study guide Rotations every 5 minutes SEGMENT ADDITION POSTULATE Symmetry MIDPOINT DISTANCE

Use the distance formula to find the perimeter of figure 1st: name all 3 coordinates

1.7 Transformation in the Coordinate Plane 9.5 Symmetry Notes: PowerPoints Practice p. 52 Think & Discuss # 2 p.53 #3-6 Practice p. 637 #3 - 8

Chapter 1 pt. 1 Review VOCABULARY ANALYZE TRANSFORMATION FIGURES Review each concept for test Use slips as a study guide Test Friday SEGMENT ADDITION POSTULATE Symmetry MIDPOINT DISTANCE

Chapter 1.1- 1.7 Test (Skip 1.3 – 4) Define Vocabulary, Sketch a picture, and Draw a real world picture Collinear and Coplanar Describe points, lines, and planes given a figure Measuring Segments: Midpoint & Distance on a number line and given a pair of coordinates

Chapter 1.1- 1.7 Test (Skip 1.3 – 4) Identify and graph reflections, rotations, and translations Symmetry: line of symmetry, rotational symmetry, & plane symmetry

Warm-Up: 2. Use the distance formula to find the perimeter of figure. 1st: name all 4 coordinates Warm-Up: 1. M is the midpoint of AB. A has coordinates (2, 2), and M has coordinates (4, -3). Find the coordinate B.

Chapter 1 pt. 1 Review VOCABULARY ANALYZE TRANSFORMATION FIGURES Review each concept for test Use slips as a study guide Test Today SEGMENT ADDITION POSTULATE Symmetry MIDPOINT DISTANCE

Part 1: VOCABULARY For each term, write two descriptions, sketch it, and give a real world example TERM DEFINITION SKETCH REAL WORLD EXAMPLE POINT 1. 2. LINE 2 SEGMENT RAY PLANE

Part 2: Analyze Figure Using the figure provided at the right, answer to the following. Are points D, C, and B collinear? __________ Are points G, D, A, and F coplanar? __________ How many planes contain A? _________ Where do plane P and plane R intersect? ________ Name four noncoplanar points. ________ Write another name for plane P. ________

Part 3: Segment Addition Postulate If B is between endpoints A and C, complete the following tasks. 1. Draw the diagram to represent the situation. 2. Write the expression to represent the situation. (What the Segment Addition Postulate would say.) _____________ = _______ 3. If AB = 15 and BC = 12, find AC. _______ 4. If BC = 13.4 and AC = 32, find AB. _______ 5. If AC = 4x + 56, BC = 22x and AB = 20, find AC. ______

Part 4: Distance 1. Which segment is congruent to segment BH? ___ A B E H I D -4 -2 0 2 4 6 8 10 Part 4: Distance Refer to the number line below to answer Questions 1 & 2. 1. Which segment is congruent to segment BH? ___ 2. Find the distance of segment BD. _________ Find the distance between each pair of points using the distance formula 3. L (11, 12) and N (8, 3) Distance: ________ 4. Distance: ________  

A B E H I D -4 -2 0 2 4 6 8 10 Part 5: Midpoint Refer to the number line below to answer Questions 1 & 2. 1. What is the coordinate of the midpoint of segment HI? _________ 2. If the midpoint of segment HC is B, what is the coordinate of C? (No, C is not on the graph. You have to figure out where it would be if it were.) Find the distance between each pair of points using the distance formula 3. L (11, 12) and N (8, 3) Midpoint: ________ 4. Midpoint: ________  

Part 6: Transformations Describe each transformation. Explain.

Part 6: Transformations 4. A figure has vertices at X(3, -3), Y(1, -2), and Z(3, 0). After a transformation, the image of the figure has vertices at X¢(-3, -3), Y¢(-1, -2), and Z¢(-3, 0). Draw the preimage and the image. Then identify the transformation. _______________ 5. . Draw and label the image of STUV after the translation of 5 units up.

Part 7: Symmetry Tell whether each figure has line symmetry. If so, draw all lines of symmetry. 1. 2. 3. Anna, Bob, and Otto write their names in capital letters. Draw all lines of symmetry for each whole name if possible. Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. 4. 5.

Chapter 1.1- 1.7 Test (Skip 1.3 – 4) Define Vocabulary, Sketch a picture, and Draw a real world picture Collinear and Coplanar Describe points, lines, and planes given a figure Measuring Segments: Midpoint & Distance on a number line and given a pair of coordinates

Chapter 1.1- 1.7 Test (Skip 1.3 – 4) Identify and graph reflections, rotations, and translations Symmetry: line of symmetry, rotational symmetry, & plane symmetry

Any last minute questions before test….?!?!? GOOD LUCK! DON’T FORGET TO DRAW FIGURE, if needed No talking during test D= M= When finish, read Chapter 1.3 - 1.4 and complete graphic organizer Exploring Angles.

Distance Midpoint BONUS: find the perimeter