1-3 and 1-4 Measuring Segments and Angles

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 | B A

4 10

Two segments with the same length are congruent.

If AB = CD, then AB ≅ CD

≅ means congruent

B A6 B A

D C6D C

Postulate 1-6 Segment Addition Postulate

If three points A, B, and C are collinear and B is

between A and C, thenAB + BC = AC

A

B

C

If GJ = 32,

• find x

• find GH

• find HJ

If AX = 45,

• find y

• find AQ

• find QX

A midpoint of a segment is a point that divides the segment into two congruent segments.

A B C

• B is the midpoint of AC

• AB BC

M is the midpoint of RT

• find x

• find RM

• find RT

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

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 180b. If OC is paired with x and OD is paired with y,

then mCOD = | x – y |

AB

DC

O

Angles can be...

Acute: 0 < x < 90

x° x°

Right: x = 90

x°

Obtuse: 90 < x < 180

x°

Straight: x = 180

Postulate 1-8 Angle Addition Postulate

• If point B is in the interior of AOC, then mAOB + mBOC = m AOC.

• If AOC is a straight angle, then mAOB + mBOC = 180.

Angles with the same measure are congruent.

If m1 = m2, then 1 2

Congruent

“curtains”