1-4 Measuring Segments and Angles

A B5 in

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

Examples—

A B C D E

CD=

BC=

EB=

DE=

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

Write the Segment Addition Postulate for the points described. Draw a

picture to help.

S is between D and P

C is between Q and R

T is between M and N

For each problem, draw a picture representing the three points and theinformation given. Solve for indicated.

If AC = 24 in. and CE = 13 in., AE = _____.

If CE = 7in. and AE = 23 in., AC = _____.

Find QR in the following problems. R is between Q and S.

If RS = 44.6 and SQ = 68.4, find QR.

If RS = 33.5 and RQ = 80, find SQ.

If GJ = 32,

• find x

• find GH

• find HJ

If AX = 45,

• find y

• find AQ

• find QX

For each problem, draw a picture representing the three points and theinformation given. Solve for indicated.

Given : AC = 39 m

A B C

2x-8 x+17

x = ________

AB = _______

BC = _______

If U is between T and B, find the value of x and the lengths of the

segments. TU = 2x, UB = 3x + 1, TB = 21

x = ______

TU = _______

UB = _______

TU = 4x-1, UB = 2x -1, TB = 5x

x = ______

TU = _______

UB = _______

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

A B C

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

AB

DC

O

Angles can be...

Acute: 0 < x < 90

x° x°

Right: x = 90

x°

Obtuse: 90 < x < 180

x°

Straight: x = 180

17

Adjacent AnglesTwo angles are called adjacent angles if they

share a vertex and a common side (but neither is inside the opening of the other).

Angles 1 and 2 are adjacent:

1 2

Postulate 1-8 Angle Addition Postulate

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

19

Example

A

M

TH

.m MAH

Angles with the same measure are congruent.

If m1 = m2, then 1 2

Congruent

“curtains”

Homework—

Page 29-33 (1, 3, 8-16, 27, 28, 59, 60, 61, 70-72, 75-78)