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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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objectives
Objectives
  • Name and label corresponding parts of congruent triangles
  • Identify congruence transformations
slide3
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 - 25
  • Pre-AP Geometry: Pg. 195 #9 – 16, 22 - 27
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…
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.

slide13

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

slide17

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

slide19

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

slide21
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 #14, 16, 18, 22 - 25
  • Pre-AP Geometry: Pg. 204 #14 – 19, 22 - 25