Warm Up 8/91. Given the following endpoints, find the midpoint.

a. (-3, -7) and (-6,2)

b. (5, -9) and (-7, -25)

2. Given the following endpoint and midpoint, find the other endpoint.

a. M(-5, 9) E(-8,9)

Simplify:

234382.4

20211.3 27

Answers:

1. a) (-4,5, -2.5)b) (-1, -17)

2. (-2,9)

3. -7

4. 46

Euclid’s Five Postulates

1) List the five postulates

2) Sketch a picture

3) State the limits of postulate #5

Postulate #1

1. A line segment can be drawn joining any two points

A

B

Postulate #2

• Any line segment can be extended indefinitely to form a line

C

D

Given line segment CD, you can extend it to make line CD

Postulate #3

• Given a line segment, a circle can be drawn having the segment as a radius and one endpoint as a center

Postulate #4

• All right angles are congruent

G

F

E

GFE

Postulate #5

• If l is any line and P is any point not on l, then there exists exactly one line through P that is parallel to l.

l

P

Limit of postulate #5

• Postulate #5 is only true in a _______ and cannot be applied to a_________

plane

curve

classwork

• Get a color paper

• markers

• Fold into fourths

• In each box write and illustrate each of Euclid’s postulates, including the limitation

• In one of the last boxes answer the following questions.

Answer each question and State which of Euclid's postulate you would use to prove the following.

1. Given HS I can make a HS?

2. Given point A and point Z how many lines can I make

3. Given the two angles, what statement can I make?

4. What shape can I make if I am given a line segment where one point is an endpoint, and I rotate the segment around the endpoint?

D

E

You must know (have memorized) the 5 postulates for test on Friday

• Homework: Make note cards on the 5 postulates. Come up with a way to help you memorize them.