Post on 25-Dec-2015
4.3 Proving Δs are : SSS and SAS
Geometry
Ms. Reser
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.
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.
Remember?
As of yesterday, Δs could only be if ALL sides AND angles were
NOT ANY MORE!!!!There are two short cuts to add.
Post. 19Side-Side-Side (SSS) post
• If 3 sides of one Δ are to 3 sides of another Δ, then the Δs are .
Meaning:
If seg AB seg ED, seg AC seg EF & seg BC seg DF, then ΔABC ΔEDF.
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A
B CE
D F
Given: seg QR seg UT, RS TS, QS=10, US=10
Prove: ΔQRS ΔUTS
Q
R S T
U
10 10
Proof
Statements Reasons
1. 1. given
2. QS=US 2. subst. prop. =
3. Seg QS seg US 3. Def of segs.
4. Δ QRS Δ UTS 4. SSS post
Post. 20Side-Angle-Side post. (SAS)
• 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, and C X, then ΔABC ΔZXY.
B
AC
X
Y
Z)(
Given: seg WX seg. XY, seg VX seg ZX,
Prove: Δ VXW Δ ZXY
1 2
W
V
X
Z
Y
Proof
Statements Reasons
1. seg WX seg. XY 1. given seg. VX seg ZX
2. 1 2 2. vert s thm
3. Δ VXW Δ ZXY 3. SAS post
Given: seg RS seg RQ and seg ST seg QT
Prove: Δ QRT Δ SRT.Q
R
S
T
Proof
Statements Reasons
1. Seg RS seg RQ 1. Given seg ST seg QT
2. Seg RT seg RT 2. Reflex prop
3. Δ QRT Δ SRT 3. SSS post
Given: seg DR seg AG and seg AR seg GR
Prove: Δ DRA Δ DRG.
D
AR
G
Proof
Statements
1. seg DR seg AG
Seg AR seg GR
2. seg DR Seg DR
3.DRG & DRA are rt. s
4.DRG DRA
5. Δ DRG Δ DRA
Reasons1. Given
2. reflex. Prop of 3. lines form 4 rt. s
4. Rt. s thm
5. SAS post.