Congruent Figures Objective: 1) To recognize figures & their corresponding parts.

Congruent FiguresCongruent Figures

Objective:

1) To recognize figures & their corresponding parts

Congruent PolygonsCongruent Polygons

Are the same size and the same shape.Are the same size and the same shape.Fit exactly on top of each otherFit exactly on top of each other

Have Have corresponding parts: corresponding parts:Matching sides and Matching sides and ss

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another

These are called translations and are covered in chapter 9

You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another

ΔΔQXT QXT ΔΔPHDPHD

QX QX PH PH

Naming PolygonsNaming Polygons

Order Matters!!Order Matters!!

AB C

DE S

TUW

R

ABCDE

WUTSR

AB

ED

B

D

A

WU

RS

U

S

W

Example: Example: ΔΔWYS WYS ΔΔMKVMKV

mmW = 25W = 25mmY = 55Y = 55Find mFind mVV

W

Y

S

M

K

V25

55

100

Example 2: Congruence StatementExample 2: Congruence Statement

Finish the following congruence statement:

ΔJKL Δ_ _ _

K

J

L

M

N

ΔJKL ΔNML

Proof: Th(4-1)Proof: Th(4-1)

If 2 If 2 s of one s of one ΔΔ are are to 2 to 2 s another s another ΔΔ, , then the third then the third s are also s are also ..

Given: Given: B B EE

A A DDProve: Prove: C C F F

A

B C

D

FE

Statements

1)1) B B E & E & A A DD

2)2) mmB + mB + mA + mA + mC = 180C = 180

mmE + mE + mD + mD + mF = 180F = 180

3) m3) mB + mB + mA + mA + mC = C =

mmE + mE + mD + mD + mF F

4)4) mmB + mB + mA + mA + mC = C =

mmB + mB + mA + mA + mFF

5)5) mmC = mC = mFF

6)6) C C FF

Reasons

1) Given

2) Def. of Δ

3) Trans.

4) Subs.

5) Subtr.

6) Def. of

Example Example

Proof:Proof:

Given: GC Given: GC GD GD

CN CN DN DN

Prove: Prove: ΔΔGCN GCN ΔΔGDNGDN

G

CN

D

G

ND

C

Show all of the parts are

3 sides

3 angles

given

given

reflexive

given

given

Thm 4-1