Warm Up

Real World Solid Figures

List up to 5 objects found in the real world that have

shapes of each of the following solid figures:

• Prism• Cube• Pyramid• Cylinder• Cone• Sphere

The distance between any two points is the absolute value of the difference of the

coordinates. 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.

A ruler can be used to measure the distance betweentwo points. A point corresponds to one andonly one number on the ruler. This number

is called a coordinate .

Postulate 1-2-1: The points on a line can be putinto a one-to-one correspondence

with the real numbers.

Example: A Ba b

So, AB= a-b = b-a

AB AC

A B A C

Ex:

A

B

C

2

2

1

What we CAN write:

AB AC

A B A C

What we CAN’T write:

AC BC

Equal=

NumbersAB

Congruent

AB

AB 2

A B 2

Notes

Shapes

Notes

A

B

C

D

FG

H

ClassworkWrite down every congruency statement.

A

B

C

D

FG

H

NotesMidpoint: The point on a segment that’s the same distance from both endpoints.

3

B CD

3D is the midpoint of BC

F

D

HH is the midpoint of FD

D

E

A A is the midpoint of DE

Notes - Midpoint FormulaHow do we find the exact center of a line segment?

(7,8)

(3,2)

(7,8)

(3,2)

x1 x22

,y1 y22

7 32,8 22

10

2,10

2

(5,5)

5,5

Notes - Midpoint FormulaLet’s make it work for us.

Notes - Midpoint FormulaHow do we find the exact center of a line segment?

x1 x22

,y1 y22

Conjecture 1: Midpoint Conjecture

If your points are and then your midpoint is:

x1,y1

x2,y2

(-9,2)

(7,-6)

x1 x22

,y1 y22

9 72

,2 62

22, 42

(-1,-2)

-1,-2

Notes - Midpoint FormulaOne more time.

Homework:

p.17 #1-10

p.19 #36-39,42-44