Proving Triangles are Congruent SSS, SAS; ASA; AAS CCSS: G.CO7.
4.3 Proving Δ s are : SSS and SAS
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Transcript of 4.3 Proving Δ s are : SSS and SAS
4.3 Proving Δs are : SSS and SAS
pg. 212
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.
Assignment