4.3 Proving Δs are : SSS and SAS Geometry Ms. Reser.
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Transcript of 4.3 Proving Δs are : SSS and SAS Geometry Ms. Reser.
![Page 1: 4.3 Proving Δs are : SSS and SAS Geometry Ms. Reser.](https://reader036.fdocument.pub/reader036/viewer/2022082408/56649ddb5503460f94ad26f3/html5/thumbnails/1.jpg)
4.3 Proving Δs are : SSS and SAS
Geometry
Ms. Reser
![Page 2: 4.3 Proving Δs are : SSS and SAS Geometry Ms. Reser.](https://reader036.fdocument.pub/reader036/viewer/2022082408/56649ddb5503460f94ad26f3/html5/thumbnails/2.jpg)
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.
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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.
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Remember?
As of yesterday, Δs could only be if ALL sides AND angles were
NOT ANY MORE!!!!There are two short cuts to add.
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Post. 19Side-Side-Side (SSS) post
• If 3 sides of one Δ are to 3 sides of another Δ, then the Δs are .
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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
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Given: seg QR seg UT, RS TS, QS=10, US=10
Prove: ΔQRS ΔUTS
Q
R S T
U
10 10
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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
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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 .
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• If seg BC seg YX, seg AC seg ZX, and C X, then ΔABC ΔZXY.
B
AC
X
Y
Z)(
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Given: seg WX seg. XY, seg VX seg ZX,
Prove: Δ VXW Δ ZXY
1 2
W
V
X
Z
Y
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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
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Given: seg RS seg RQ and seg ST seg QT
Prove: Δ QRT Δ SRT.Q
R
S
T
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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
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Given: seg DR seg AG and seg AR seg GR
Prove: Δ DRA Δ DRG.
D
AR
G
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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.