UNIT 1. Basics of Geometry. What is a pattern? Aug 20 11:14 AM. Jun 8 2:09 PM. Aug 20 10:46 AM. Aug 20 11:08 AM. 1.1 Finding and Describing Patterns
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1 UNIT 1 Basics of Geometry 1.1 Finding and Describing Patterns What is a pattern? Jun 8 2:09 PM Aug 20 11:00 AM Aug 20 10:46 AM Aug 20 11:04 AM Let's Practice! Making predictions! Describe a pattern. 3. Aug 20 11:08 AM Aug 20 11:14 AM 1
2 Time to practice! Guided Practice Activity (click on the paw to launch) Aug 20 11:24 AM Aug 20 11:29 AM Classwork page 5 # 1-10 Please be sure to read the directions carefully! BELLWORK Describe the pattern and write the next number you expect to see in the pattern. 1. 1, 5, 25, 125,... Homework pages 5-6 # even Please be sure to read the directions carefully! 2. 1, 2, 4, 7, 11, , -5, -2, 1, , 1, 2, 6, 24, 120, Aug 20 1:30 PM Jan 24 11:00 AM 1.2 Inductive Reasoning: Looking for patterns and making conjectures. What is a conjecture? A conjecture is an unproven statement that is based on a pattern or observation. Jan 24 11:07 AM Aug 20 1:35 PM 2
3 Group Activity: Work with your group of four to count the number of ways that 3 people can shake hands. What about 4 people? Complete the table with these numbers. People Handshake 1?? 10 Let's summarize that activity: Much of the reasoning in geometry consists of three stages. 1) Look for a pattern Look at several examples. Use diagrams and tables to help discover a pattern. 2) Make a conjecture Use the examples to make a general conjecture. 3) Verify the conjecture Use logical reasoning to verify that the conjecture is true in ALL cases. (This will come later...) Look for a pattern in the table. Write a conjecture about the number of ways that 6 people can shake hands. Aug 20 1:42 PM Aug 20 1:49 PM Complete the conjecture. You try one... Conjecture: The sum of any two odd numbers is. Complete the conjecture based on the pattern in the examples. Conjecture: The product of any two odd numbers is. Examples: 1 x 1 = 1 3 x 5 = 15 3 x 11 = 33 Conjecture: The sum of the first n odd positive integers is. 7 x 9 = x 11 = x 15 = 15 Aug 20 1:52 PM Aug 20 1:54 PM What is a counterexample? Show the conjecture is false by finding a counterexample. Conjecture: The sum of two numbers is always greater than the larger of the two numbers. A counterexample is an example that shows a conjecture is false. Hint: Always think about 0 and 1!!! Conjecture: All shapes with four sides the same length are squares. Notes: A conjecture is considered if it is not ALWAYS true. To prove a conjecture is false, you need to find only counterexample. Aug 20 1:35 PM Aug 20 1:57 PM 3
4 You try! Show the conjecture is false by finding a counterexample _eworkbook/randomproblems.html If the product of two numbers is even, the numbers must be even. If a shape has two sides the same length, it must be a rectangle. Aug 20 2:07 PM Jan 24 10:59 AM Bellwork. Classwork: page 11 #1-6 Homework: page #8, 14, 16, 18, 22, 24, 38, 40 Show that the conjecture is false by finding a counterexample. 1. All rectangles with an area of 12 square feet have the same perimeter. 2. If the sum of two numbers is positive, then the numbers must be positive. 3. The absolute value of a number is always positive. 4. The quotient of two positive integers is a positive integer. Aug 20 2:09 PM Jan 25 12:36 PM 1.3 Points, Lines, and Planes What is a point? Draw a point here. -A point is a in space. -A point has no dimension. -Represented by a small. -Named by capital letter. What is a line? -A line extends in opposite directions with no end. Its length cannot be measured. -A line has dimension. It has no width. -Represented using arrows on the ends -Named by capital letters or lower case cursive letter. Draw a line here. Aug 20 2:12 PM Aug 10 9:35 PM 4
5 What is a plane? -A plane is a flat surface with no thickness -A plane has dimensions -A plane extends in all directions with no end -Represented by a shape that looks like a floor or wall. -Named by cursive CAPTIAL letter or by non-collinear points. Draw a plane here. Aug 20 2:43 PM Aug 10 9:35 PM Postulates 1 & 2 Postulate 1 Words Through any two points there is exactly one line. Symbols Line n passes through points P and Q. P Q n Collinear Points are points that lie on the same line I N O R l m Postulate 2 Words Through any three points not on a line there is exactly one plane. P T Symbols Plane T passes through points A, B, and C. A B a) Any two points are collinear!! C T b) Name each line two ways Aug 20 2:49 PM Aug 10 9:42 PM F) Points and lines in the same plane are coplanar. B C Name three points that are collinear. H Name four points that are coplanar. A D F F G E H a) Any three points are coplanar!! b) name a plane that contains segment FG? Name three points that are not collinear. D G E Name the plane. c) Name the planes that contain D? Aug 10 9:42 PM Aug 20 2:55 PM 5
6 Segment part of a line with two endpoints. C G CG represents the measure of the segment CG represents the picture of the segment Word Diagram Name line segment ray Ray one endpoint, extends indefinitely in one direction B A AB Aug 10 11:27 AM Aug 20 3:23 PM Draw three noncollinear points J, K, and L. Then draw line JK, line segment KL, and ray LJ. Guided practice activity Aug 20 3:30 PM Aug 20 3:32 PM Classwork page 17 #1 14 all Bellwork 1. 9, 3, 3,, 2. Find a counterexample for... All triangles have a right angle. Homework pages #16 56 even 3. 3x 12 = /4 x + 3 = (x 5) = 35 Aug 20 3:33 PM Jan 29 12:19 PM 6
7 1.4 Sketching Intersections In your groups, let's complete the activity on page 21 in your book. Each group will need: 3 note cards 1 pair of scissors pencil For your answers, each group will need: one white board one dry erase marker Jan 29 12:24 PM Aug 20 3:35 PM Intersection: the point or points that the figures have in common Postulate 3 Words If two lines intersect, then their intersection is a. Symbols Lines s and t intersect at point P. s Name the intersection of line AC and line BE. Name the intersection of line BE and line DF. A D B E C F P t Postulate 4 Words If two planes intersect, then their intersection is a. Name the intersection of line AC and line DF. Symbols Planes M and N intersect at line d. Aug 20 3:40 PM Aug 20 3:47 PM Sketch a plane. Then sketch each of the following. a) a line that is in the plane b) a line that does not intersect the plane c) a line that intersects the plane at a point Aug 20 3:49 PM Aug 20 3:52 PM 7
8 You try: a) sketch three lines that lie in a plane Guided practice: pages # odd b) sketch two lines that intersect a plane at the same point c) sketch two planes that do not intersect Aug 20 3:53 PM Aug 20 3:56 PM Classwork page 25 #1-6 all Homework pages #10-32 even Bellwork 1. What is the intersection of lines AB and BC? 2. What is the intersection of planes AED and HGC? 3. Name the intersection of planes AEH, HGC, and ABC. 4. Name the planes that intersect in line AD. Aug 20 3:54 PM Feb 1 11:37 AM 1.5 Segments and their Measures Distance and Length Distance is the absolute value of the difference of the coordinates of A and B. Notes: the distance from point A to point B would be written as AB AB is also called the length of AB Aug 20 3:58 PM Aug 20 4:59 PM 8
9 BELLWORK Take a ruler and measure the segments on p. 31 #7 12 in both inches and centimeters Aug 20 5:00 PM Feb 4 11:20 AM What does the word between mean? ` Aug 20 5:02 PM Aug 20 5:06 PM Aug 20 5:09 PM Aug 20 5:09 PM 9
10 Congruent Segments segments that have the same length A C B D Notes: The length AB is equal to the length CD. Segment AB is congruent to segment CD. Aug 20 5:09 PM Aug 20 5:15 PM Guided practice activity Aug 20 5:16 PM Aug 20 5:18 PM Classwork page 31 # 1-6 Homework pages # 8-28 even, 32 (challenge) Bellwork A X B E D 1. If AB = 14, XB = 10, find AX. 2. Find BE if AB = 14 and AE = Are AX and BE congruent? If so, show why or why not. 4. XE = 15 and ED = 4, find XD. 5. If L, M, and N are collinear and LM = 30, NM = 10, and LN = 20, which point is between the other two points? Aug 20 5:20 PM Feb 5 10:56 AM 10
11 1.6 Angles and Their Measures Protractor activity Now that we've reviewed how to use a protractor, let's complete the activity on page 34 of your book with your group. Each group will need: 4 sheets of notebook paper one colored pencil one protractor For your answers, each group will need: one white board one dry erase marker Aug 20 5:21 PM Aug 20 5:32 PM What is an angle? An angle consists of two rays that have the same endpoint. Naming Angles Side Vertex Side Aug 20 5:24 PM Aug 20 5:23 PM Congruent Angles: angles that have the measure Acute Angles: angles between 0 degrees and 90 degrees Right Angle: angles that have a measure of degrees Obtuse Angle: angles between 90 degrees and degrees Straight Angle: angles that have a measure of degrees Aug 20 5:35 PM Aug 20 5:36 PM 11
12 Angle Addition Postulate Aug 20 5:40 PM Aug 20 5:41 PM Aug 20 5:42 PM Aug 20 5:42 PM Classwork: Unit 1 Test Review page 38 # 1-14 Group flash card review Homework: pages # 15, 18, 20, 24, 26, 28, 29, 30 All students work on the following: page 42 #1-12 pages # even I will call groups up individually to participate in the Triangle Factory Game. Winning group will receive 2 bonus points on tomorrow's test! Aug 20 5:43 PM Aug 20 5:46 PM 12
13 Aug 21 12:07 PM Feb 11 12:28 PM Feb 11 12:28 PM Feb 11 12:28 PM Feb 11 12:28 PM Feb 11 12:28 PM 13
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