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Quiz Homework 1. Quiz Homework 1 Quiz Homework 1.

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Presentation on theme: "Quiz Homework 1. Quiz Homework 1 Quiz Homework 1."— Presentation transcript:

1

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 )


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