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

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

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

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R M T 5x+9 8x-36 M Lesson 1-5: Examples 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 Example 3 Using Midpoint M is the midpoint of segment RT. Find RM, MT, and RT.

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Vocabulary and Key Concepts Postulate 1-7: Protractor Postulate Postulate 1-8: Angle Addition Postulate (m

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Vocabulary and Key Concepts Acute Angle: measures between 0 0 and 90 0 Right Angle: measures exactly 90 0 Obtuse Angle: measures between 90 0 and 180 0 Straight Angle: measures exactly 180 0 Congruent angles: two angles with the same measure x0x0 Lesson 1-6: Measuring Angles x0x0 ACUTE ANGLE RIGHT ANGLE 0 < x < 90 0 x = 90 0 x0x0 90 0 < x < 180 0 OBTUSE ANGLE x0x0 x = 180 0 STRAIGHT ANGLE

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Example 1 Naming Angles Lesson 1-6: Examples NN ame can be the number between the sides of the angle. <3 A G 3 C

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Example 2 Measuring and Classifying Angles Lesson 1-6: Examples Find the measure of each

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Example 3 Using the Angle Addition Postulate Lesson 1-6: Examples Suppose that m<1=42 and m

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Example 4 Identifying Angle Pairs Lesson 1-6: Examples In the diagram, identify pairs of numbered angles as: Complementary angles form 90 0 angles. <3 and <4 5 1 2 3 4 Supplementary angles form 180 0 angles. Vertical angles form an “X”. <1 and <2<2 and <3 <1 and <3

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Example 5 Making Conclusions From A Diagram Lesson 1-6: Examples Can you make each conclusion from a diagram? 3 m

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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

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B A D C Vocabulary Perpendicular lines are two lines that intersect to form right angles. Lesson 1-7: Measuring 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. N L K J

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T Example 1 Constructing Congruent Segments Lesson 1-7: Examples Construct segment TW congruent to segment KM. STEP 1: Draw a ray with endpoint T. KM STEP 2: Open the compass the length of segment KM. 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.

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Example 2 Constructing Congruent Angles Lesson 1-7: Examples Construct

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Example 3 Constructing The Perpendicular Bisector Lesson 1-7: Examples Given segment AB. Construct line XY so that line XY is perpendicular to segment AB at the midpoint M of segment AB. 1.Put the compass point on point A and draw a long arc. Be sure the opening is greater than half of AB. 2.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. 3.Draw line XY. The point of intersection of segment AB and line XY is M, the midpoint of segment AB. A B X Y M

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Example 4 Finding Angle Measures Lesson 1-7: Examples Line WR bisects

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

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Reference Textbook: Prentice Hall Mathematics GEOMETRY by Bass, Charles, Hall, Johnson, Kennedy PowerPoint Created by Mrs. Crespo Accelerated Algebra/Geometry Mrs. Crespo 2012-2013

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