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.