Warm UpSimplify.

1. 7 – (–3) 2. –1 – (–13)3. |–7 – 1|

Solve each equation.

4. 2x + 3 = 9x – 11 5. 3x = 4x – 5

6. How many numbers are there between and ?

1

2

3

4

Warm UpSimplify.

1. 7 – (–3) 2. –1 – (–13)3. |–7 – 1|

Solve each equation.

4. 2x + 3 = 9x – 11 5. 3x = 4x – 5

6. How many numbers are there between and ?

1

2

3

4

10 12 8

x = 2 x = 5

Infinitely many

coordinate midpointdistance bisectlength segment bisectorconstructionbetweencongruent segments

Vocabulary

A ruler can be used to measure the distance between two points. A point corresponds to one and only one number on a ruler. The number is called a coordinate. The following postulate summarizes this concept.

The distance between any two points is always positive. Therefore, we can say that the distance between the points is the absolute value of the difference of the coordinates.

AB = |a – b| or |b - a|

A

a

B

b

If the coordinates of points A and B are a and b, then the distance between A and B is |a – b| or |b – a|. The distance between A and B is also called the length of AB, or AB.

Congruent segments are segments that have the same length.

Use compass only – no ruler – to create congruent segments

Create congruent segments on your notes (lightly show tick mark).

Key Concept – Be careful …

PQ represents a number (or distance) while represents a geometric figure (line segment).

PQ

Be sure to use equality for numbers (PQ = PQ) while we use congruence for figures

PQ ≅PQ

In order for you to say that a point B is between two points A and C, all three points must lie on the same line (which is to say they are collinear) and AB + BC = AC.

M is between N and O. Find NO. The key to solving this is the segment addition postulate which says than NM + MO = NO

The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments.

If M is the midpoint of AB, then AM = MB.

So if AB = 6, then AM = 3 and MB = 3.

Bisect a segment with a compass …

Lesson Quiz

1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

2. S is the midpoint of , TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV.

TV

3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

Lesson Quiz

1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

2. S is the midpoint of , TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV.

TV

3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

NO = 22.6

Lesson Quiz

1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

2. S is the midpoint of , TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV.

TV

3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

TS = 25, SV = 25 and TV = 50

Lesson Quiz

1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

2. S is the midpoint of , TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV.

TV

3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

x = 3

Assignment today is page 17: 12-15, 20-29, 35-41 and 48-49.

Remember that homework help is always available at http://www.thinkcentral.com/index.htm

Today’s keyword is “MG7 1-2”.