Download Day 3 1.3 Segment Addition

CCSS Geom Unit A Day 3 Seg AdditionA.notebook
D.I.R.T?
August 19, 2014
Day 3 Segment Addition
Segment Addition Postulate
Learning Targets:
I can use the segment addition postulate to find the length of segments.
I can apply the definition of congruent, midpoint, and bisect to find the length of segments. CCSS: G­CO.1 CLE: N.2.D.
Performance Standard 1.6, 3.4, 3.5 DOK­1
Knowledge MA 3
Buddy Books today!!!!
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
August 19, 2014
PROPERTIES OF EQUALITY
PROPERTIES OF EQUALITY
ADDITION: If a=b, then a+c = b + c
MULTIPLICATION: If a = b, then a
c = bc
SUBTRACTION: If a = b, then a ­ c = b ­ c
DIVISION: If a = b, then a/c = b/c
.
(1)
(2)
PROPERTIES OF CONGRUENCE
PROPERTIES OF CONGRUENCE
REFLEXIVE: a = a
TRANSITIVE: If a = b and b = c then
a = c.
.
SYMMETRIC: If a = b then b = a
SUBSTITUTION: If a=b you can replace one with the other.
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
PROPERTIES OF CONGRUENCE
August 19, 2014
Other Properties
DISTRIBUTIVE: a (b+c) = ab + ac
Segment Addition: XY + YZ = YZ
Angle Addition: m<AOB + m<BOC = m<AOC
Vertical angles are congruent.
Linear pairs are supplementary.
Ruler postulate: The distance between any two points is measureable.
A segment has two ENDPOINTS, therefore it can be MEASURED!
Segment AB = 3 inches long
A B
If segments can be measured, then their lengths can be compared. If two segments have the same length then we say the segments are CONGRUENT.
Congruent segments: two segments with the same length. Actual measurements are considered EQUAL not congruent.
Use the congruent symbol with letters:
Use the equal signs with numbers:
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
A B
C D
­8 ­5
­2 0 3
August 19, 2014
E
1) Find AC.
2) Find BE.
3) Find CE.
4) AB ≅ ______.
A
BC≅ ______
AB = ______
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B
C
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
August 19, 2014
Segment Addition postulate: If 3 points are collinear, then AB + BC = AC.
C
B
A
Do you see why you need to Know the Gab?
An important fact of understanding geometric figures: coding and labeling!!! Mark all information in a figure that you understand from the information given.
Examples: Label and code all information. Solve for the value(s).
5) A
C
CT= 10
AT=2
CA=?
T
6)
D
7)
E
S
F
T
G
DT=60
DS=2x­8
ST=3x­12
X=
DS=
DT=
EF=2x­6
FG=x+7
EG=25
x=
EF=
FG=
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
8) Given AC = 36
August 19, 2014
3x
2x + 1
B
A
Statement
Reason
1. AC = 36
1. Given
2. AB + BC = AC
2. 3. 3x + 2x + 2 = 36
4. 5x + 1 = 36
5. 5x = 35
6. x = 7
3. C
4. 5. 6. Segment addition Proofs
9) EG = 100, Find the value of x.
Statement
.E .F
4x­20
2x + 30
.G
Reason
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
August 19, 2014
Midpoint­ the point that divides a segment into two congruent segments. M is the midpoint of AB. Label and code.
10) D
11)
P
O
G
T
Q
O is the midpoint of DG. DO= 2x+11
OG=3x­4 Find:
DO=
OG=
DG=
T is the midpoint of PQ.
PT= 5x+3
TQ=7x­9
Find PT.
12) C is the midpoint of AB. AC = 2x + 1 and CB = 3x ­ 4. Find AC, BC and AB. Draw a picture and label. Show all work. Box answers.
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CCSS Geom Unit A Day 3 Seg AdditionA.notebook
August 19, 2014
Name the property of equality or congruence that justifies each statement
13) <K≅<K
14) If 2x­8 = 10, then 2x = 18
15) If RS ≅ TW and TW ≅ PQ, then RS ≅ PQ
16) If m<A = m<B, then m<B =m<A
What did you learn today?
Can I use the segment addition postulate to find the length of segments?
Can I apply the definition of congruent, midpoint, and bisect to find the length of segments? 8