2. Quiz Homework 1

3. Quiz Homework 1

4. 1.2-1.3 Using Segments, Congruence, midpoints and Distance
Learn Segment Postulates so you can identify segment congruence.
Learn midpoint and distance formulas so you can find measurements in coordinate plane

5. Vocab:
In the study of geometry, definitions, postulates and undefined terms are accepted as true w/o verification or proof.
These 3 types of statements can be used to prove that theorems are true.
Proof – logical argument backed by statements that are accepted as true.
3 types of proofs-paragraph (informal), 2 column (used most often) and flow chart
Congruence – means equal. We can say that 2 lines that have the same measure are “congruent”. We use the symbol

6. Segment Addition Postulate
Ruler Postulate
The pts on any line can be paired with real numbers so that given any 2 pts P and Q on the line. P corresponds to zero and Q corresponds to a positive number.
Segment Addition Postulate
If Q is between P and R, then PQ + QR = PR
If PQ + QR = PR, then Q is between P and R

7. Using a straight edge and compass only:
Draw a segment in your notes using a straight edge.
Now, using a straight edge and compass, construct a segment congruent to the one you drew without using the markings on the ruler side of your straight edge.
Explain how you did it 
Using your straight edge and compass, construct a picture to explain the segment addition postulate and how it works.

8. Example
Find LM if L is between N and M, NL = 6x – 5, LM = 2x + 3 and NM = 30. Prove each step!
Hint: Draw a picture L N M
6x - 5
2x + 3 30
6x – 5 + 2x + 3 = 30
8x – 2 = 30
8x = 32
x = 4
Segment addition postulate
Substitution
Addition property
Division property
LM = 2(4) + 3
= 11
Substitution
Substitution

9. Vocab:
*Midpoint – point of a segment that divides the segment into 2 equal parts.
*Segment bisector – is a point, ray, line, line segment or plane that intersects the segment at its midpoint.

10. Example Definition of midpoint VM = MW 4x-1 = 3x + 3 Substitution
Point M is the midpoint of Find the length of
V M W
4x x+3
VM = MW
4x-1 = 3x + 3
x – 1 = 3
x = 4
VM = 4x – 1
VM = 4(4) – 1
VM = 15 units
Definition of midpoint
Substitution
Subtraction property
Addition property
Given
Did we answer the question?

11. To find the midpoint on coordinate plane
Use the midpt formula:
Example
Find the midpt of between (-3,-4) and (5,7)
M = (1,1.5)

12. To find the coordinates of end pt given midpt.
Use the midpt formula, but solve for a different variable.
Example
Find Q given RQ if P(4,-1) and R(3,-2).
(5,0)

13. Your Turn: Your Turn: (0,-3) Find Q given NQ if L(4,-6) and N(8,-9).
If y is midpt of xz, xy = 2x+11 and yz=4x-5, find xz
2x + 11 = 4x - 5
16 = 2x
8 = x
xz = 2(27)
= 54
xy = 2(8) + 11
= 27

14. Distance Formula Commit this to memory…You are going to need it 
X coordinate from pt # 1
X coordinate from pt # 2
Y coordinate from pt # 2
Y coordinate from pt # 1
Commit this to memory…You are going to need it 

15. Example
Find JK if J(9,-5) and K(-6,12)
Distance formula:

16. Homework www.classzone.com Put this in your agenda u/n:columbiageo
p/w: wildcat
Put this in your agenda
Pg – 26, 28
Pg , (show the properties), 17-19, 24-27, 31-33
(31 problems total for 2 days…doable )