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.

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Presentation transcript:

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  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: | − |  The distance between A and B is called the length.

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.

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

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.

1-3: Measuring and constructing angles

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, by a point on each ray and the vertex, or by a number.

 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. exteriorinterior  The measure of an angle is usually given in degrees. Terms continued

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. A B O

Types of angles Acute AngleRight AngleObtuse Angle Straight Angle Measures greater than 0 degrees and less than 90 degrees. Measures 90 degrees. Measures greater than 90 degrees and less than 180 degrees. Formed by 2 opposite rays and measures 180 degrees.

terms  Congruent angles are angles that have the same measure.  An angle bisector is a ray that divides an angle into 2 congruent angles.

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