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LESSONS 1-5 TO 1-7

LESSONS 1-5 TO 1-7. Accelerated Algebra/Geometry Mrs. Crespo 2012-2013. Recap Postulate 1-5: Ruler Postulate Postulate 1-6: Segment Addition Postulate (AB+BC=AC) Definition of Coordinate, Congruent Segments and Midpoint. B. A. C. A. B. C. Lesson 1-5: Measuring Segments. 2. 0.

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LESSONS 1-5 TO 1-7

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  1. LESSONS 1-5 TO 1-7 Accelerated Algebra/Geometry Mrs. Crespo 2012-2013

  2. Recap • Postulate 1-5: Ruler Postulate • Postulate 1-6: Segment Addition Postulate (AB+BC=AC) • Definition of Coordinate, Congruent Segments and Midpoint. B A C A B C Lesson 1-5: Measuring Segments 2 0 -2

  3. Example 1 Comparing Segment Lengths • Example 2 Using Addition Segment Postulate If AB=25, find x. Then, find AN and NB. x+7 A N 2x-6 B AN = 2x – 6 = 2(8) – 6 = 16 – 6 = 10 NB = x + 7 = 8 +7 = 15 AN + NB = AB (2x-6) +( x+7) = 25 3x + 1 = 25 3x = 24 x = 24/3 x = 8 Lesson 1-5: Examples

  4. Example 3 Using Midpoint M is the midpoint of segment RT. Find RM, MT, and RT. M 8x-36 5x+9 RM = MT 5x + 9 = 8x – 36 5x – 8x = -36 – 9 -3x = -45 x = -45/-3 x = 15 RM = 5x + 9 = 5(15) + 9 = 75 + 9 = 84 MT = 8x – 36 = 8(15) – 36 = 120 – 36 = 84 RT = RM + MT = 84 + 84 = 168 R T M Lesson 1-5: Examples

  5. Vocabulary and Key Concepts • Postulate 1-7: Protractor Postulate • Postulate 1-8: Angle Addition Postulate (m<AOB + m<BOC = m<AOC) • Definition of Angle Formed by two rays with the same endpoint. B A O C B 1 T Q Lesson 1-6: Measuring Angles

  6. Vocabulary and Key Concepts • Acute Angle: measures between 00 and 900 • Right Angle: measures exactly 900 • Obtuse Angle: measures between 900 and 1800 • Straight Angle: measures exactly 1800 • Congruent angles: two angles with the same measure x0 x0 x0 x0 STRAIGHT ANGLE OBTUSE ANGLE RIGHT ANGLE ACUTEANGLE Lesson 1-6: Measuring Angles x = 1800 x = 900 900< x < 1800 0 < x < 900

  7. Example 1 Naming Angles • Name can be the number between the sides of the angle. C • Name can be the vertex of the angle. G • Name can be a point on one side, the vertex, and a point on the other side of the angle. A <3 3 Lesson 1-6: Examples <G <AGC or <CGA

  8. Example 2 Measuring and Classifying Angles • Find the measure of each <AOC. • Classify as acute, obtuse, or straight. C OBTUSE ACUTE C B A B A Lesson 1-6: Examples O O 600 m<AOC = 1500 m<AOC =

  9. Example 3 Using the Angle Addition Postulate • Suppose that m<1=42 and m<ABC=88. Find m<2 A m<1 + m<2 = m<ABC 42 + m<2 = 88 m<2 = 88-42 m<2 = 460 1 2 B C Lesson 1-6: Examples

  10. Example 4 Identifying Angle Pairs • In the diagram, identify pairs of numbered angles as: Complementary angles form 900 angles. <3 and <4 1 2 Supplementary angles form 1800 angles. 5 3 <2 and <3 <1 and <2 4 Vertical angles form an “X”. Lesson 1-6: Examples <1 and <3

  11. Example 5 Making Conclusions From A Diagram • Can you make each conclusion from a diagram? A <A <C <B and <ACD are supplementary. B C D m<BCA + m<DCA = 1800 Lesson 1-6: Examples segment AB segment BC 3

  12. Vocabulary • Construction is using a straightedge and a compass to draw a geometric figure. • A straightedge is a ruler with no markings on it. • A compass is a geometric tool used to draw circles and parts of circles called arcs. Lesson 1-7: Basic Construction

  13. Vocabulary • Perpendicular lines are two lines that intersect to form right angles. • A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby, bisecting the segment into two congruent segments. • An angle bisector is a ray that divides an angle into two congruent coplanar angles. A D B C J K Lesson 1-7: Measuring Angles N L

  14. Example 1 Constructing Congruent Segments • Construct segment TW congruent to segment KM. K M STEP 1: Draw a ray with endpoint T. STEP 2: Open the compass the length of segment KM. T W STEP 3: With the same compass setting, put the compass point on point T. Draw an arc that intersects the ray. Label the point of intersection W. Lesson 1-7: Examples

  15. Example 2 Constructing Congruent Angles • Construct <Y so that <Y is congruent to <G. <Y <G Draw a ray with endpoint Y. With the compass point on G, draw an arc that intersects both sides of <G. Label the points of intersection E and F. With the same compass setting, put the compass point on point Y. Draw an arc that intersects the ray. Label the point of intersection Z. Open the compass to the length EF. Keeping the same compass setting, put the compass on point Z. Draw an arc that intersects with the arc previously. Label the point of intersection X. Draw ray YX to complete <Y. X E 750 750 G Y F Z Lesson 1-7: Examples

  16. Example 3 Constructing The Perpendicular Bisector • Given segment AB. Construct line XY so that line XY is perpendicular to segment AB at the midpoint M of segment AB. Put the compass point on point A and draw a long arc. Be sure the opening is greater than half of AB. With the same compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect as an X and Y. Draw line XY. The point of intersection of segment AB and line XY is M, the midpoint of segment AB. X A B M Lesson 1-7: Examples Y

  17. Example 4 Finding Angle Measures • Line WR bisects <AWB so that m<AWR=x and m<BWR=4x-48. Find m<AWB. m<AWR = x = 16 m<AWR = m<BWR x = 4x – 48 -3x = -48 x = 16 A m<BWR = 4x – 48 = 4(16) – 48 = 64 – 48 = 16 R x 4x – 48 W Lesson 1-7: Examples B So, m<AWB = m<AWR + m<BWR = 16 + 16 = 32

  18. HW: Posted on Edline Accelerated Algebra/Geometry Mrs. Crespo 2012-2013

  19. Reference Textbook: Prentice Hall MathematicsGEOMETRY by Bass, Charles, Hall, Johnson, KennedyPowerPoint Created by Mrs. Crespo Accelerated Algebra/Geometry Mrs. Crespo 2012-2013

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