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 (<capital letter), by a point on each ray and the vertex (< 3 capital letters), or by a number(<#).

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

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.

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. 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.

ANGLE ADDITION POSTULATE If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

HOMEWORK Homework: pg. 17 #12-32 even pg. 24 #4-24 multiples of 4, 18, 30