4 3 s
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4.3  Δ s. Objectives. Name and label corresponding parts of congruent triangles Identify congruence transformations.  Δ s. Triangles that are the same shape and size are congruent. Each triangle has three sides and three angles.

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4.3  Δ s

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4 3 s

4.3 Δs


Objectives

Objectives

  • Name and label corresponding parts of congruent triangles

  • Identify congruence transformations


4 3 s

Δs

  • Triangles that are the same shape and size are congruent.

  • Each triangle has three sides and three angles.

  • If all six of the corresponding parts are congruent then the triangles are congruent.


Cpctc

CPCTC

  • CPCTC –

    Corresponding Parts of Congruent Triangles are Congruent

  • Be sure to label Δs with proper mappings (i.e. if D  L, V  P, W  M, DV  LP, VW  PM, and WD  ML then we must write ΔDVW ΔLPM)


Congruence transformations

Congruence Transformations

  • Congruency amongst triangles does not change when you…

  • slide,

  • turn,

  • or flip

  • … the triangles.


Assignment

Assignment

  • Geometry: Pg. 195 #9 – 16, 22 - 27

  • Pre-AP Geometry:Pg. 195 #9 – 16, 22 – 27, 29 - 30


So to prove s must we prove all sides all s are

So, to prove Δs  must we prove ALL sides & ALL s are  ?

Fortunately, NO!

  • There are some shortcuts…


4 4 proving s are sss and sas

4.4 Proving Δs are  : SSS and SAS


Objectives1

Objectives

  • Use the SSS Postulate

  • Use the SAS Postulate


Postulate 4 1 sss side side side postulate

Postulate 4.1 (SSS)Side-Side-Side  Postulate

  • If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .


More on the sss postulate

E

A

F

C

D

B

More on the SSS Postulate

If seg AB  seg ED, seg AC  seg EF, & seg BC  seg DF, then ΔABC ΔEDF.


Given qr ut rs ts qs 10 us 10 prove qrs uts

Given: QR  UT, RS  TS, QS = 10, US = 10Prove: ΔQRS ΔUTS

Example 1:

U

U

Q

Q

10

10

10

10

R

R

S

S

T

T


4 3 s

Example 1:

Statements Reasons________

1. QR  UT, RS  TS,1. Given

QS=10, US=10

2. QS = US 2. Substitution

3. QS  US 3. Def of segs.

4. ΔQRS ΔUTS 4. SSS Postulate


Postulate 4 2 sas side angle side postulate

Postulate 4.2 (SAS)Side-Angle-Side  Postulate

  • If 2 sides and the included  of one Δ are  to 2 sides and the included  of another Δ, then the 2 Δs are .


More on the sas postulate

More on the SAS Postulate

  • If seg BC  seg YX, seg AC  seg ZX, & C X, then ΔABC  ΔZXY.

B

Y

)

(

A

C

X

Z


Given wx xy vx zx prove vxw zxy

Given: WX  XY, VX  ZX Prove: ΔVXW ΔZXY

Example 2:

W

Z

X

1

2

V

Y


4 3 s

Example 2:

Statements Reasons_______

1. WX  XY; VX  ZX 1. Given

2. 1 2 2. Vert. s are 

3. Δ VXW Δ ZXY 3. SAS Postulate

W

Z

X

1

2

V

Y


Given rs rq and st qt prove qrt srt

Given: RS  RQ and ST  QT Prove: Δ QRT  Δ SRT.

Example 3:

S

Q

R

T


4 3 s

Example 3:

Statements Reasons________

1. RS  RQ; ST  QT 1. Given

2. RT  RT 2. Reflexive

3. Δ QRT Δ SRT 3. SSS Postulate

Q

S

R

T


Given dr ag and ar gr prove dra drg

Given: DR  AG and AR  GRProve: Δ DRA  Δ DRG.

Example 4:

D

R

A

G


4 3 s

Statements_______

1. DR  AG; AR  GR

2. DR  DR

3.DRG & DRA are rt. s

4.DRG   DRA

5. Δ DRG  Δ DRA

Reasons____________

1. Given

2. Reflexive Property

3.  lines form 4 rt. s

4. Right s Theorem

5. SAS Postulate

Example 4:

D

R

G

A


Assignment1

Assignment

  • Geometry: Pg. 204 #7, 8, 10, 14 – 16, 22 - 25

  • Pre-AP Geometry:Pg. 204 #12, 14 – 18, 22 - 25


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