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Chapter 1 Section 3 Parts of Lines

Chapter 1 Section 3 Parts of Lines. Monday 9/8 -Warm Up Get your lap top and go to Mrs. Baumher’s Geometry Quia Page. Save the link in your favorites. http://www.quia.com/pages/geometrybaumher.html Make note cards for the distance formula and midpoint formula. Homework Answers.

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Chapter 1 Section 3 Parts of Lines

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  1. Chapter 1 Section 3Parts of Lines Monday 9/8 -Warm Up Get your lap top and go to Mrs. Baumher’s Geometry Quia Page. Save the link in your favorites. http://www.quia.com/pages/geometrybaumher.html Make note cards for the distance formula and midpoint formula.

  2. Homework Answers P. 526 2-16 even 2. 5 4. 5 6. 8. 13 10. 12. 4 14. yes, c 16. no p. 545-6 1-11 odd 1. (3,3) 3. (0, -2) 5. (1.9, 0.4) 7. , -5/4, (-1,-3) 9. 17, -15/8, (-3, 7/2) 11. (9,5)

  3. Recall from last week… Other Spatial Relationships • Skew: lines that are non-coplanar and never intersect • Three Lines and Intersection: Concurrent

  4. N M Recall from last week… • A line is a set of infinite points extending in opposite directions. • Properties: • No Thickness or length • Infinite • Notation: Two points: MN Lower case letter: line l Diagrams:

  5. Parts of Lines – Line Segment Notation: AB A B Segment AB contains points A and B and the set of all points between A and B. A and B are endpoints of the segment.

  6. Parts of Lines – Ray Ray AB contains AB and all other points P such that B is between A and P. A ray has one endpoint and is infinite in one direction. Notation: AB A B P

  7. Parts of Lines – Opposite Rays Given 3 collinear points, R, S, and T; If S is between R and T, then SR and ST are opposite rays. R T S Opposite rays share a common endpoint.

  8. Parts of Lines – Length The Length of AB is the distance between points A and B. A B 5in Notation: AB Example: AB = 5 inches Can you find the length of a line? No! Can you find the length of a ray? No!

  9. Notice the difference in notation for each… Notation Line AB AB Segment AB AB Ray AB AB The length of AB AB

  10. Congruent A AB @ CD AB = CD 5in 5in B C D In geometry, two figures that have the same shape and size are congruent. Notation: @ Example: Congruent segments would have equal lengths.

  11. Parts of Lines – Midpoint of a Segment A C B If C is the midpoint, then AC @ CB. The midpoint of a segment is the point that divides a segment into two congruent segments. AC = CB

  12. Algebra Connection – Midpoint of a Segment C 2x - 3 5x - 24 A B Given that C is the midpoint of AB, find x. Because C is the midpoint, AC = CB. Use this information to set up an algebraic equation: AC = CB 2x – 3 = 5x – 24 Now solve for x. 7 = x

  13. Parts of Lines – Segment Bisector D C is the midpoint of AB. C B A CD is the bisector of AB. A segment bisector is a line, segment, ray, or plane that intersects the given segment at its midpoint.

  14. Segment Addition Postulate A B C If B is between A and C, then… AB + BC = AC

  15. Geometry/Trig 2 – Algebra Connection I. II. C A T D O G A is the midpoint of CT CA = 8x - 6 AT = 3x + 24 DO = 3x + 1 OG = 8x - 1 DG = 22 Find the following: 1.) x = ___________ 2.) CA = __________ 3.) AT = __________ 4.) CT = __________ Find the following: 1.) x = ___________ 2.) DO = __________ 3.) OG = __________ III. IV. P E T M T H A PE = 5x ET = 4x - 6 PT = x + 26 MA = TH MA = 2x AT = 4x MH = 3x + 30 Find the following: 1.) x = ________ 2.) MA = ________ 3.) TH = ________ 4.) MH = ______ 5.) MT = ________ 6.) AH = ________ 7.) AT = ______ Find the following: 1.) x = ___________ 2.) PT = __________ 3.) PE = __________ 4.) ET = __________

  16. Geometry/Trig 2– Segment Addition Algebra Connection F GH bisects DF H E G D Find the value of x. 1. DE = 5x + 3 EF = 33 x = _____ 2. DE = 45 EF = 5x – 10 x = _____ 3. DE = 3x EF = x + 6 x = _____ 4. DE = 2x – 3 EF = 5x – 24 x = _____ Find the value of y. 5. GE = y EH = y – 1 GH = 11 y = _______ 6. GE = 3y EH = 24 GH = 7y – 4 y = ______

  17. CoolDown Create your flashcards of today’s important vocabulary Get your worksheet checked

  18. Geometry Trig 2 – Foundational Vocabulary Review I. Name the following 1. Name a line. 2. Name a line segment. 3. Name a ray. 4. Name a plane. 5. Name a point. 6. Name two parallel lines. 7. Name two intersecting lines. 8. Name two skew lines. 9. Name two parallel planes. 10. Name the plane parallel to plane DBCF. II. Choose the word from the word bank that matches the description below. -Word Bank- Collinear Coplanar Protractor Space Perpendicular Lines Skew Lines Ruler Parallel Lines 11. Two non coplanar lines that do not intersect. 15. Points that lie on the same plane. 12. The instrument used to measure angles. 16. Two coplanar lines that do not intersect. 13. Two lines that intersect to form right angles. 17. The set of all points. 14. Points that lie on the same line. 18. The instrument used to measure a short distance.

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