1-2: Measuring & Constructing Segments

RULER POSTULATEThe 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:

| − |𝒂 𝒃 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 POSTULATEIf 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.

exterior interior

• 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 Angle Right Angle Obtuse 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 evenpg. 24 #4-24 multiples of 4, 18, 30