4.3 Proving ?s are ? : SSS and SAS

1
4.3 Proving ?s are ? SSS and SAS

• Geometry
• Fall 2005
• Mrs. Spitz

2
Standards/Benchmarks

• Standard 2 Students will learn and apply
  geometric concepts
• Objectives
• Prove that triangles are congruent using the SSS
  and SAS Congruence Postulates.
• Use congruence postulates in real life problems
  such as bracing a structure.

3
Assignment

• Worksheet 4.2 A back to back with 4.3 A
• Reminder there is a quiz after section 4.4
• There are 7 sections in this chapter.
• 4.4 and 4.5 are one section
• 4.6 and 4.7 are another section
• This makes your test likely to be next Monday.
• Deficiencies go out the end of this week.

4
Remember?

• As of yesterday, ?s could only be ? if ALL sides
  AND angles were ?
• NOT ANY MORE!!!!
• There are two short cuts to add.

5
Post. 19Side-Side-Side (SSS) ? post

• If 3 sides of one ? are ? to 3 sides of another
  ?, then the ?s are ?.

6
Meaning
A
___
___ ___ ___

• If seg AB ? seg ED, seg AC ? seg EF seg BC ?
  seg DF, then ?ABC ? ?EDF.

B
C
___ ___
E
___ ___ ___
___
___ ___
D
F
7
Given seg QR ? seg UT, RS ? TS, QS10,
US10Prove ?QRS ? ?UTS

U
Q
10
10
R
S
T
8
Proof

• Statements Reasons
• 1. 1. given
• 2. QSUS 2. subst. prop.
  
• 3. Seg QS ? seg US 3. Def of ? segs.
  
• 4. ? QRS ? ? UTS 4. SSS post

9
Post. 20Side-Angle-Side post. (SAS)

• If 2 sides and the included ? of one ? are ? to 2
  sides and the included ? of another ?, then the 2
  ?s are ?.

10

• If seg BC ? seg YX, seg AC ? seg ZX, and ?C ? ?X,
  then ?ABC ? ?ZXY.

B
Y
)
(
C
A
X
Z
11
Given seg WX ? seg. XY, seg VX ? seg ZX, Prove
? VXW ? ? ZXY
W
Z
X
1
2
Y
V
12
Proof

• Statements Reasons
• 1. seg WX ? seg. XY 1. given
  seg. VX ? seg ZX
• 2. ?1 ? ?2 2. vert ?s thm
• 3. ? VXW ? ? ZXY 3. SAS post

13
Given seg RS ? seg RQ and seg ST ? seg QTProve
? QRT ? ? SRT.
S
Q
R
T
14
Proof

• Statements Reasons
• 1. Seg RS ? seg RQ 1. Given seg ST ? seg
  QT
• 2. Seg RT ? seg RT 2. Reflex prop ?
  
• 3. ? QRT ? ? SRT 3. SSS post

15
Given seg DR ? seg AG and seg AR ? seg
GRProve ? DRA ? ? DRG.
D
R
A
G
16
Proof

• Statements
• seg DR ? seg AG
• Seg AR ? seg GR
• 2. seg DR ? Seg DR
• 3.?DRG ?DRA are rt. ?s
• 4.?DRG ? ? DRA
• 5. ? DRG ? ? DRA

• Reasons
• Given
• reflex. Prop of ?
• ? lines form 4 rt. ?s
• 4. Rt. ?s thm
  
• 5. SAS post.