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Section 1-4: Measuring Segments and Angles

Section 1-4: Measuring Segments and Angles. Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems. Essential Questions. 1.) How do you find the length of a segment on a number line ? 2.) How do the midpoint and bisector of a segment differ ?

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Section 1-4: Measuring Segments and Angles

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  1. Section 1-4: Measuring Segments and Angles Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems.

  2. Essential Questions • 1.) How do you find the length of a segment on a number line? • 2.) How do the midpoint and bisector of a segment differ? • 3.) How are angles identified and classified?

  3. length of a segment • the distance between two points P and Q, denoted PQ or QP, on a number line is the absolute value of the difference of their coordinates. • P coordinate – Q coordinate  or Q coordinate – P coordinate 

  4. congruent segments • segments that have equal length •  is read segment DE is congruent to segment FG

  5. midpoint of a segment • the point that divides a segment into two congruent segments

  6. bisector of a segment • a line, ray, segment, or plane that intersects the segment at its midpoint

  7. angle • the union of two rays which have the same endpoint • The two rays are called the sides of the angle. (Use rays to name the sides of angles and the endpoint must be the vertex.) Their common endpoint is the vertex.

  8. angle • Three sets of points make up an angle: the interior, exterior, and the angle itself. • The symbol  is used for an angle. Usually three capital letters are used to name an angle (may use a number or the vertex as a single letter). Never use only two letters to name an angle. If using three letters, use a letter on the two different sides of the angle.

  9. acute angle • an angle with degree measure m such that 0 < m < 90

  10. right angle • an angle with degree measure m = 90. (Use a little box in the vertex of the angle to indicate a right angle on a diagram.)

  11. obtuse angle • an angle with degree measure m such that 90 < m < 180

  12. straight angle • an angle with degree measure m = 180

  13. congruent angles • angles that have equal measures • For example:  1  2 means m  1  m 2 • *Note: Indicate that angles are congruent on a diagram by drawing an arc at the vertex in the interior of the angles with a corresponding number of tick marks (slashes) through the arcs.

  14. Examples P. 29, 30 • 1, 3 • DO 2, 4 • 5 • DO 6, 7 • 12 • DO 14 • Pairs do p 30 (16 – 26)

  15. Segment Addition Postulate • B is between A and C iff AB + BC = AC. A B C

  16. 8) If RS = 15 and ST = 9, then RT = • 10) a. If RS = 3x + 1, ST = 2x – 2, RT = 64. Find x. b. Find RS and ST. • Do 9, 11

  17. Angle Addition Postulate • If point B lies in the interior of  AOC, then m  AOB + m  BOC = m  AOC. A B O C

  18. 27) Find m<CBD if m<ABC = 45 and m< ABD = 79. • 28) Find m<GFJ if m<EFG = 110. • Do p 31 (42 – 48, 65, 66)

  19. Homework • Practice 1-4 • Mixed review, p 33 (87 – 97)

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