geometry notes day 4
TRANSCRIPT
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1IntrotoGeometryDay4Congruence/Triangles
Warmup:
Whatdotheseallhaveincommon?
HowdothesedifferfromOrks?
c.istheonlyork
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2a.
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3b.
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4Agooddefinition...
isprecise.Avoidsvaguewordslikesome,small,orrounded.
placesinobjectinacategory,anddescribeshowitdiffersfromotherthingsinthecategory.
Example:Ahexagonisapolygonwith6sides.category howitdiffers
isreversible.Forexample,wecouldsay
Apolygonwith6sidesisahexagon
ThereverseiscalledtheCONVERSEofthestatement.Inagooddefinition,theconversewillalsobetrue.
Howcoulditnotbetrue?
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5Workwithyourpartner/grouptowriteagooddefinitionforeachgeometricterminthehandout.
Youarefinishedwhenyou...
AGREEonthedefinition
and
WRITEitdown.
Note:thehashmarksonasideindicatethatthesidesarecongruent.
C
A
T
Thesemarksmeanthat
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6righttriangle:
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7
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8
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9
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10
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median:
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13
median:
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Summary
Sides
Angles
None
Scalene
Two
Isosceles
Three
Equilateral
AllAcute
Acute
OneObtuse
ObtuseOneRightRight
AnytriangleisclassifiedwithBOTH.(Whichpairsareimpossible?)Let'sDrawA....
IsocelesRight ScaleneObtuse
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Attachments
Lesson41adapted.pdf
Practice41.pdf
Activity910DefiningTriangles.pdf
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Geometry Lesson 4-1 Daily Notetaking Guide L146
Vocabulary and Key Concepts.
Theorem 41
If two angles of one triangle are congruent to
two angles of another triangle, then
Congruent polygons are
Examples.
Naming Congruent Parts ABC QTJ. List the congruent corresponding parts.
List the corresponding sides and angles in the same order.
Angles: A Q B J
Sides:
Using Congruency XYZ KLM, mY 67, and mM 48. Find mX.
Use the Triangle Angle-Sum Theorem and the definition of congruentpolygons to find mX.
mX mY mZ Triangle Angle-Sum Theorem
mZ Corresponding angles of congruent triangles are congruent.
mZ Substitute 48 for mM.
mX 180 Substitute.
mX 180 Simplify.
mX Subtract 115 from each side.
2
ACTJAB > QT
T
J
QB
A C
1
H
GI
D
E F
B C
AD
E F
Lesson Objective
Recognize congruent figures and theircorresponding parts
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NAEP 2005 Strand: Geometry
Topic: Transformation of Shapes and Preservation ofProperties
Local Standards: ____________________________________
Lesson 4-1 Congruent Figures
Name_____________________________________ Class____________________________ Date________________
P
ears
on
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47Daily Notetaking Guide Geometry Lesson 4-1L1
Name_____________________________________ Class____________________________ Date ________________
Pea
rso
n E
du
cati
on
, In
c., p
ub
lish
ing
as
Pear
son
Pre
nti
ce H
all.
All
rig
hts
res
erve
d.
Finding Congruent Triangles Can you conclude that ABC CDE?List corresponding vertices in the same order.
If ABC CDE, then BAC .
The diagram above shows BAC , not DCE.
The statement ABC CDE true.
Notice that , , and .
Also, CBA and BAC .
Using Theorem 4-1, you can conclude that ECD .
Since all of the corresponding sides and angles are congruent, the triangles
are congruent. The correct way to state this is ABC .
Quick Check.
1. WYS MKV. List the congruent corresponding parts. Use three lettersfor each angle.
Sides: WY MK
Angles: WSY MVK
2. It is given that WYS MKV. If mY 35, what is mK? Explain.
mK
3. Can you conclude that JKL MNL? Justify your answer.
K
J
L
N
M
ACBABC
3
B
3
A
4C 4 D
3
E
SMART Notebook
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Geometry Chapter 4 Lesson 4-1 Practice 1
Name Class Date
Practice 4-1 Congruent FiguresEach pair of polygons is congruent. Find the measures of the numberedangles.
1. 2. 3.
kCAT O kJSD. List each of the following.
4. three pairs of congruent sides
5. three pairs of congruent angles
WXYZ O JKLM. List each of the following.
6. four pairs of congruent sides
7. four pairs of congruent angles
State whether the pairs of figures are congruent. Explain.
8. GHJ and IHJ 9. QRS and TVS
10. Developing Proof Use the information given in the diagram.Give a reason that each statement is true.
a. L Qb. LNM PNQc. M Pd. , , e. LNM QNP
PNMNQNLNQPLM
Q
R
V
TS
95
95
G
H
I
J
7
56 8
140
A
B G
F
Y X D E
3
135
50R UP W
M N S T
Q V
4
G
L I
H
120
110
K J
1
2
A
F C
B
E D
P
ears
on
Ed
uca
tio
n, I
nc.
, pu
blis
hin
g a
s Pe
arso
n P
ren
tice
Hal
l.A
ll ri
gh
ts r
eser
ved
.
C
A
D
S
JT
MW
Z
Y
X
J
KL
L M
QP
N
SMART Notebook
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SMART Notebook
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