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1 -3 and 1-4 Measuring Segments and Angles

1 -3 and 1-4 Measuring Segments and Angles. B. A. 4. 10. Postulate 1-5 Ruler Postulate The point of a line can be put into a one-to-one correspondence with the real number so that the distance between any two points is the absolute value of the difference of the corresponding numbers .

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1 -3 and 1-4 Measuring Segments and Angles

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  1. 1-3 and 1-4 Measuring Segments and Angles

  2. B A 4 10 Postulate 1-5 Ruler Postulate The point of a line can be put into a one-to-one correspondence with the real number so that the distance between any two points is the absolute value of the difference of the corresponding numbers. AB = | a – b |

  3. B B D 6 A A C 6 D C Two segments with the same length are congruent.If AB = CD, then AB ≅ CD≅ means congruent

  4. C B A Postulate 1-6 Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, thenAB + BC = AC

  5. If GJ = 32, • find x • find GH • find HJ • If AX = 45, • find y • find AQ • find QX

  6. A B C A midpoint of a segment is a point that divides the segment into two congruent segments. • B is the midpoint of AC • AB  BC • M is the midpoint of RT • find x • find RM • find RT

  7. An angle is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). Angles are measured in degrees. Sides are GC and GA; G is the vertex. • Name this angle: • G • 3 • CGA • AGC

  8. D C O B A Postulate 1-7 Protractor Postulate Let OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180 in such a way that: a. OA is paired with 0 and OB is paired with 180 b. If OC is paired with x and OD is paired with y, then mCOD = | x – y |

  9. x° x° Acute: 0 < x < 90 Right: x = 90 x° x° Straight: x = 180 Obtuse: 90 < x < 180 Angles can be...

  10. Postulate 1-8 Angle Addition Postulate • If point B is in the interior of AOC, then mAOB + mBOC = m AOC. • If AOC is a straight angle, then mAOB + mBOC = 180.

  11. Angles with the same measure are congruent. If m1 = m2, then 1 2 Congruent “curtains”

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