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Transcript
Section: 1.2 Name: Topic: Points, Lines and Class: Geometry 1A Planes Period: Standard: 1 Date: Points 1. In the space below put a point and label it Point A. A point is a __________ at a specific _________________. Segments 2. Mark another point as Point B. 3. Connect Point A to Point B. This is _______________ AB or _____. A ___________________ is a _____________ of a line with _______ endpoints. Lines 4. Draw two more points C and D and draw a line through these points. A line extends in two directions ___________________. We write this ________. Note: Although a ________________ can be measured by its length, a ________ cannot since it goes on _______________. Rays 5. A ray is a part of a line that goes on forever in one _________________. Draw Ray EF or ______ in the space above. In this case, the ray starts at E and continues past_________. (This is ______ the same as starting at F and continuing past Point E.) 1 Examples Name each point, line, segment and ray. G J N K _______________ and M __________ can be named in two ways. H L Draw two points, A and B, on your piece of patty paper. Fold the patty paper so that you get a line through your two points. How many points does it take to determine a line? Did you need another point to make the line? What if you had only had one point? Place a third point, C, on the line. The three points, A, B and C, are called __________________ because they are all on the ____________ _____________. Choose a point, D, not on line AB. Fold a line through C and D. What is the least number of points it takes to form a line? ______ (glue your patty paper here) Name as many lines as you can. Naming a Line 2 Planes Imagine the sheet of patty paper extending in all __________________ forever. This is the idea behind a plane. Naming a Plane You name a plane with a cursive capital letter or with three points. 1. Name your patty paper Plane P. 2. Fold plane P anywhere on the paper. Now we have two different planes. Label the second plane R. 3. Glue your patty paper in the space below. Only glue down Plane P. What is the intersection of two planes? Where do the two planes intersect? Place points S and T on this intersection. Mark Point U in Plane P and Point V in Plane R. How many points does it take to make a plane? You must have _________ points that are _____-_____________ to make a plane. What is another name for Plane P? _______________________ What is another name for Plane R? _______________________ Could we name either plane as Plane ST? Why? How many planes can pass through line ST? ________________ 3 Examples Use the picture below to determine planes, lines and points. F G H E D A C B A. Shade Plane DCA. B. Name Plane DCA another way. _______________________ C. Name the intersection of Plane HGC and Plane EFG. ______ D. Name the intersection of EF and DF . ________ E. List all points that are on Plane FGC. ___________________ F. Mark Point J so that it is collinear with Points A and D. More on Rays We know that a ray is a _________ of a line that extends in _________ direction forever. What happens when you have two rays that share their endpoint? There are three different ways this could happen. Case 1: A(n) ________________ is formed. Case 2: A(n) ________________ is formed. Case 3: A(n) ________________ is formed. Summary/Reflection: Why do you think arrowheads are used when drawing or naming a line? 4 Section: 1.3 Name: Topic: Parallel Lines & Class: Geometry 1A Planes Period: Standard: 1 Date: F G H E D A Parallel Lines & Segments C B EF and HG are parallel segments. What makes two lines or segments parallel? ___________________________________ Name every segment parallel to DC . _____________________ Perpendicular Lines & Segments EF and EA are perpendicular segments. What makes two lines or segments perpendicular? _______________________ Name a segment perpendicular to DC . ____________________ Skew Lines & Segments EF and HB are skew segments. What makes two segments or lines skew? _______________________________________ Name all segments skew to DC . _________________________ Parallel Planes Planes DCA and FGH are parallel planes. What makes two planes parallel? ______________________________________ Name a plane parallel to Plane DCF. ______________________ Summary/Reflection: Are all lines either intersecting or parallel? Explain. 5 Section: 1.4A Name: Topic: Measuring Class: Geometry 1A Segments Period: Standard: 1 & 12 Date: Bisect a Segment 1. On your patty paper use a straightedge to draw AB . 2. Fold the patty paper so that Point A falls on Point B. Crease the fold to form a line. The fold line is the _________________ of AB . _________________ The point where the fold intersects AB is the ______________ of AB . Label this point C. _________________ We can mark the two __________________ segments with tick marks or write AC _____ CB . Copy a Segment 3. Fold your patty paper so that you can trace over AB . 4. Mark the new segment A ' B ' . The prime marks signify which points are _______________________. When you copy a segment you make another segment with the same _____________________. We can say AB _____ A ' B ' . 5. Glue your patty paper in the space below. 6 Coordinate on a Number Line The coordinate of a point is its _________________ and ___________________ from the ______________ (0) on a number line. Examples A -5 B 0 5 The coordinate of point A is -1. A. What is the coordinate of point B? ________ B. Label point C at -4 and point D at 6. Length of a Segment The distance from one point to another is the length of the segment joining them. The distance is given by the formula Absolute value sign The length of AB . AB ______ ______ The coordinate of A. Examples The coordinate of B. C. AB ______ ______ = ______________ = _______ D. AC = __________________________________________ E. CD = __________________________________________ Midpoint To find the midpoint of a segment take the average of the two endpoints. Midpoint of AB = AB 2 Examples The midpoint of AB = _____ _____ = ________ 2 F. What is the midpoint of AC? G. What is the midpoint of CD? 7 Segment Addition If three points A, B and C are collinear and B is between A and C, then AB + BC = ____________. Draw a picture to help you understand the postulate. Example A J, M and D are collinear. D is between J and M. JD = 5. JM = 13. What is DM? 1. Draw a picture. 2. Set up an equation. 3. Solve and check. Example B A, C and T are collinear. A is between C and T. CT = 26. A is the midpoint of CT . What is AT? Example C A, N and T are collinear. N is between A and T. AN = 2x – 6. NT = x + 7. AT = 25. What is x? _______ What is AN? ______ What is NT? ______ Measuring with a Ruler Throughout this course you will need to measure segments with a ruler. There are two units of measure we’ll use in this class – _______________ and ______________________________. The crayon is about ________ inches long. The pencil is about _______ centimeters long. 8 Inches Inches are broken down into smaller fractional units. Segments are usually measured in sixteenths of an inch, such as 5 10 . 8 16 1 4 or 4 16 What is the measurement of the segment shown below? Centimeters Centimeters are broken down into smaller units called millimeters. There are _______ millimeters in one centimeter. How many centimeters are shown in the brace below? _______ Examples Measure each segment below in inches and centimeters. A. B. Summary/Reflection: On a number line, point Q has a coordinate 1 and T has a coordinate 17. A is the midpoint of QT , B is the midpoint of QA , C is the midpoint of QB , and D is the midpoint of QC . What is the coordinate of D? 9 Section: 1.4B Name: Topic: Measuring Angles Class: Geometry 1A Period: Standard: 1 & 12 Date: Angles (_______) An angle is formed by two ___________ that share a common endpoint. This endpoint is called the ____________ of the angle. B 1 A C Naming an Angle There are many ways to name this angle - _______, _______, ______ or _______. Protractor One way to measure angles is in degrees (____). A protractor is the tool used to ___________________ the opening of an angle. MAKE A PROTRACTOR Use fraction circles to make a protractor. The measure for 0 is already marked for you. Measurement of angles is done counterclockwise. 1. Since a circle is 360 you can divide that by 2 to get the measure of half a circle. Mark it on your protractor. 2. If we split the circle into 3 parts. How big is each angle? Mark the protractor with these angles. 3. Now split the circle into 4 parts and mark it. 4. Split the circle into 6 parts and mark it. (Yes, we are skipping 5 parts.) 5. Split the circle into 8 parts and mark it. 6. Split the circle into 12 parts and mark it. 0 10 A common protractor is shown below. Notice that only the top half of the protractor is used but two sets of numbers are displayed. The ______________ of the angle is in the center of the small circle at the bottom and the ______________ of the angle lines up with the 0-180 line. If you start from the left, you’ll use the _________ set of numbers. Starting from the right, you’ll use the __________ set of numbers. Examples Use a protractor to measure the angles. A. B. 11 Types of Angles Angles can be categorized by their measure. Name of Angle Degree Measure Picture Acute Right Obtuse Straight Congruent Angles and Angle Bisectors 1. Using a straightedge draw an obtuse angle in the middle of a large piece of patty paper. Label your angle DEF. An angle bisector creates _______ _______ ______________. DEG _______ GEF 2. Fold ray DE onto ray EF. The fold should go through point E. 3. Label the fold line EG where G is in the interior of DEF. 4. Glue your patty paper into the space below. Angle Addition Postulate If point G is in the interior of DEF, then m_______ + m_______ = m DEF. 12 If point B is in the interior of AOC and AOC is a straight angle, Straight Angles then mAOB + mBOC = ___________. A O C Examples A. In the picture below mDBC = 42 and mABD =73. What is mABC? A D B C B. In the picture below mEFG = 102 and ray FH is an angle bisector. What is mHFG? E H F G Summary/Reflection: Michael says that the angles measures in the picture below must be wrong, since the first angle is “bigger” than the second. Explain in 2 – 3 sentences why Michael is incorrect in this thinking. Angle 1 Angle 2 90 180 13 Section: 2.5 Name: Topic: Proving Angles Class: Geometry 1A Congruent Period: Standard: 1 & 12 Date: 4 3 5 6 2 1 12 11 7 8 10 9 Vertical Angles In the diagram above, 1 & 12 are vertical angles, while 1 & 11 are not. Name other vertical angles: _____ & _____ _____ & _____ _____ & _____ _____ & _____ _____ & _____ Vertical angles are formed by ______________________ lines. Vertical angles share a ___________________, but not a _______________. Vertical angles are always ________________________. Adjacent Angles In the diagram above, 1 & 11 are adjacent angles. Name three other sets of adjacent angles: _____ & _____ _____ & _____ _____ & _____ Adjacent angles share one ___________________ and their _______________. Adjacent angles are _______ always ____________________. 14 Examples Which angles below are adjacent? Explain why the others are not adjacent. A. B. 3 1 4 2 C. 6 5 Complementary D. 7 8 The sum of complementary angles is ___________. C The sum of supplementary angles is ___________. Supplementary S A linear pair is ______ adjacent ____________________ angles. Linear Pair Examples A. x 120 B. 2x C. 5x + 10 70 2x – 5 15 Assumptions What can you assume from a picture? Picture OK to Assume 1 2 NOT OK to Assume 3 4 5 6 Ways to remember Complementary =90° and Supplementary = 180° Summary/Reflection: Can vertical angles be complimentary? Can vertical angles be supplementary? Draw a picture to back up your claim. 16