1 / 22

# 4.3  Δ s - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about ' 4.3  Δ s' - rocco

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 4.3 Δs

• Name and label corresponding parts of congruent triangles

• Identify congruence transformations

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 –

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)

• Congruency amongst triangles does not change when you…

• slide,

• turn,

• or flip

• … the triangles.

• Geometry: Pg. 195 #9 – 16, 22 - 27

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

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

Fortunately, NO!

• There are some shortcuts…

### 4.4 Proving Δs are  : SSS and SAS

• Use the SSS Postulate

• Use the SAS 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 .

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: ΔQRS ΔUTS

Example 1:

U

U

Q

Q

10

10

10

10

R

R

S

S

T

T

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

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

• 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: ΔVXW ΔZXY

Example 2:

W

Z

X

1

2

V

Y

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: Δ QRT  Δ SRT.

Example 3:

S

Q

R

T

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: Δ DRA  Δ DRG.

Example 4:

D

R

A

G

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

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

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