1IntrotoGeometryDay4Congruence/Triangles

Warmup:

Whatdotheseallhaveincommon?

HowdothesedifferfromOrks?

c.istheonlyork

2a.

3b.

4Agooddefinition...

isprecise.Avoidsvaguewordslikesome,small,orrounded.

placesinobjectinacategory,anddescribeshowitdiffersfromotherthingsinthecategory.

Example:Ahexagonisapolygonwith6sides.category howitdiffers

isreversible.Forexample,wecouldsay

Apolygonwith6sidesisahexagon

ThereverseiscalledtheCONVERSEofthestatement.Inagooddefinition,theconversewillalsobetrue.

Howcoulditnotbetrue?

5Workwithyourpartner/grouptowriteagooddefinitionforeachgeometricterminthehandout.

Youarefinishedwhenyou...

AGREEonthedefinition

and

WRITEitdown.

Note:thehashmarksonasideindicatethatthesidesarecongruent.

C

A

T

Thesemarksmeanthat

6righttriangle:

7

8

9

10

11

12

median:

13

median:

14

Summary

Sides

Angles

None

Scalene

Two

Isosceles

Three

Equilateral

AllAcute

Acute

OneObtuse

ObtuseOneRightRight

AnytriangleisclassifiedwithBOTH.(Whichpairsareimpossible?)Let'sDrawA....

IsocelesRight ScaleneObtuse

Attachments

Lesson41adapted.pdf

Practice41.pdf

Activity910DefiningTriangles.pdf

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

1

NAEP 2005 Strand: Geometry

Topic: Transformation of Shapes and Preservation ofProperties

Local Standards: ____________________________________

Lesson 4-1 Congruent Figures

Name_____________________________________ Class____________________________ Date________________

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

.

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

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

SMART Notebook

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