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1-2: Measuring & Constructing Segments

1-2: Measuring & Constructing Segments. RULER POSTULATE. The points on a line can be put into a one-to-one correspondence with the real numbers. Those points are called coordinates. TERMS.

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1-2: Measuring & Constructing Segments

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  1. 1-2: Measuring & Constructing Segments

  2. RULER POSTULATE • The points on a line can be put into a one-to-one correspondence with the real numbers. • Those points are called coordinates.

  3. TERMS • The distance between any two points is the absolute value of the difference of the coordinates. (cannot have a negative distance) • If the coordinate of A is a and the coordinate B is b, then the distance would be: |𝒂 − 𝒃| • The distance between A and B is called the length.

  4. TERMS CONTINUED • Congruent segments are segments that have the same length. • In order for you to say that a point B is between two points A and C, all 3 of the points must lie on the same line, and AB + BC = AC.

  5. SEGMENT ADDITION POSTULATE If B is between A and C, then AB + BC = AC.

  6. MORE TERMS • The midpoint M of AB is the point that bisects, or divides, the segment into 2 congruent segments. • A segment bisector is any ray, segment, or line that intersects a segment at its midpoint. It divides the segment into 2 equal parts at its midpoint.

  7. 1-3: Measuring and constructing angles

  8. terms • An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex. • You can name an angle several ways: by its vertex (<capital letter), by a point on each ray and the vertex (< 3 capital letters), or by a number(<#).

  9. Terms continued • The set of all points between the sides of the angle is the interior of an angle. • The exterior of an angle is the set of all points outside the angle. exterior interior • The measure of an angle is usually given in degrees.

  10. Protractor postulate Given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180.

  11. Types of angles

  12. terms • Congruent angles are angles that have the same measure. Arc marks are used to show that the 2 angles are congruent. • An angle bisector is a ray that divides an angle into 2 congruent angles.

  13. Angle addition postulate If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

  14. Homework • Homework: pg. 17 #12-32 evenpg. 24 #4-24 multiples of 4, 18, 30

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