1.2

What Is It Called?

Pg. 7Common Vocabulary Words for Geometry

Today you are going to build on your previous knowledge to answer new questions.

1.6 – SOLVING VARIABLESWhen solving an equation, start with distribution. Then combine like terms on each side of the equal sign. Afterwards, get the variable on one side of the equal sign, undo any addition, subtraction. Then undo any multiplication or division.

5 5

x = 3

x = 8

+7 +7 4x = 32

4 4

x = 9

+6 +62x = 182 2

2x – 6 = 12

–3x –3x

–2 = 6x – 14 +14 +14

12 = 6x__ __ 6 6

2 = x

e. 7x + 7 – 3x – 9 = 50

4x +2 +2

4x = 52__ __ 4 4x = 13

– 2 = 50

f. 5(x – 3) + 9x = 3x + 29 5x – 15 + 9x = 3x + 29

14x – 15 = 3x + 29 –3x –3x 11x – 15 = 29 +15 +15

11x = 44 __ __11 11

x = 4

3a = 18

a = 6

3 3

4x = 48

x = 12

4 4

4y = 3y + 30-3y -3y

y = 30

1.5 – QUADRATICSTo factor, look for the greatest common factor that divides into each term with a “hockey stick.” Then, if possible, use a t-chart to complete.

5

3x – 1

5(3x – 1)

4x

x – 6

4x (x – 6)

2x2

3x + 2

2x2 (3x + 2)

x

x

+5

+1

(x + 5)(x + 1)

2x

x

+1

+3

(2x + 1)(x + 3)

2x

x

+1

–3

(2x + 1)(x – 3)

1.8 – SOLVING BY FACTORINGWhen a quadratic equation has an equal sign, then you can solve for the variable. You can either take the square root of both sides or by using split, set, see what you get.

x

x

+7

–7

x + 7 = 0 x – 7 = 0

x = –7 x = 7

x

x

+3

–3

x + 3 = 0 x – 3 = 0

x = –3 x = 3

x + 1 = 0 x – 3 = 0

x = -1 x = 3

x

x

+6

+1

x + 6 = 0 x + 1 = 0

x = -6 x = -1

x

x

-3

-3

x – 3 = 0 x – 3 = 0

x = 3 x = 3

3x

x

-4

-1

3x – 4 = 0 x – 1 = 0

x = 4/3x = 13x = 4

Term Definition Picture Notation

Ray    

____ capital letters

AB

C D

Initial point, then continues in one direction

2

AB

DC

Term Definition Picture Notation

Opposite Rays    

AB

CRays that go in opposite directions

AB

AC

and

Term Definition Picture Notation

Segment     AB

Has two endpoints, doesn’t go on forever

AB

BA

Term Definition Picture Notation

Congruent    

AB

CD

Same shape and size

AB CD

1.9 – RAYS 1. Name the rays.

AB BA ST

2. Name a pair of opposite rays.  

YX and YZ

1.10 – SEGMENTS 1. Name the segments two different ways.

AB

BA

PO

OP

2. Draw at least two of your own examples of what segments look. Make sure you draw two points on the segment, both on the two endpoints.

A

B

C

D

1.11 – REVIEW

1. Name two rays shown in the figure.

NX

NR

2. Name the opposite ray for NM.

NC

3. Name a segment.

AN

1.12 – REVIEW Determine whether each statement is always, sometimes, or never true.

Never

Sometimes

Never

Always

never

Sometimes

1.13 – USING RULERS 1. Make sure each person gets a ruler.

2. Examine the ruler. Notice one side is measured in inches and one is measured in centimeters.

3. Find the location of centimeters. Then notice where the 0 is.

4. Line up the ruler to one end of the segment and measure how long the segment is. Each mark represents 0.1 cm. The segment below is 5.2 cm.

5. Measure the segments below in centimeters using your ruler.

5.4cm 3.3cm

1.2cm 5.7cm

4.4cm 1.7cm

2cm 2.5cm