proving lines parallel - white plains middle school · proving lines parallel november 25, 2014 ....
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Proving Lines Parallel
November 25, 2014
SWBAT: Write proofs involving Parallel and Perpendicular lines
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SWBAT: Write proofs involving Parallel and Perpendicular lines
SWBAT: Write proofs involving Parallel and Perpendicular lines
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SWBAT: Write proofs involving Parallel and Perpendicular lines
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SWBAT: Write proofs involving Parallel and Perpendicular lines
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C.A.’s A.I.A’s C.A.’s
S.S.I.A’s supp. A.E.A’s
S.S.E.A’s supp.
SWBAT: Write proofs involving Parallel and Perpendicular lines
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C.A.’s lines
A.I.A’s lines
C.A.’s lines
S.S.I.A’s supp. lines
A.E.A’s lines
If S.S.E.A’s supp. lines
Ex 7: Given: ∡1 ∡2 ∡3 ∡1 Prove: XY || WV
SWBAT: Write proofs involving Parallel and Perpendicular lines
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Reasons Statements
2. Transitive Property (1)
1. Given
2. ∡2 ∡3
3. AIA’s ∥
1. ∡1 ∡2, ∡3 ∡1
3. XY ∥ WV
(Converse of AIA Thm.)
SWBAT: Write proofs involving Parallel and Perpendicular lines
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Reasons Statements
1. ∡1 suppl. ∡3 1. Given
2. ∡2 suppl. ∡3 2. Linear Pair Thm.
3. Congruent Suppl. Thm 3. ∡1 ∡2
4. a ∥ b 4. CA’s ∥
(Converse of CA Thm.)
SWBAT: Write proofs involving Parallel and Perpendicular lines
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Reasons Statements
1. 1. Given
2. ∡BCF suppl. ∡FCD 2. Linear Pair Thm.
4. AD ⊥ CF
3. ∡s & suppl. rt ∡s
5. BE ∥ CF 5. Converse of ⊥ 𝑇𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑇ℎ𝑚 (1, 4)
( )
3. ∡BCF & ∡FCD
are rt ∡s
4. rt ∡s ⊥ lines
SWBAT: Write proofs involving Parallel and Perpendicular lines
OR
SWBAT: Write proofs involving Parallel and Perpendicular lines
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Reasons Statements
1. 1. Given
2. ∡BCF suppl. ∡FCD 2. Linear Pair Thm.
4. AD ⊥ CF
3. ∡s & suppl. rt ∡s
5. ∡BCF ≅ ∡ABE 5. All right ∡s
3. ∡BCF & ∡FCD
are rt ∡s
4. ⊥ lines rt ∡s 4. ∡ABE is a rt ∡
6. 𝐵𝐸 ∥ 𝐶𝐹 6. CA’s ∥
(Converse of CA Thm.)
SWBAT: Write proofs involving Parallel and Perpendicular lines
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Reasons Statements
1. 1. Given
2. p ∥ q 2. AIA’s ∥ (Converse of AIA Thm.)
3. s ⊥ p 3. ⊥ 𝑻𝒓𝒂𝒏𝒔𝒗𝒆𝒓𝒔𝒂𝒍 𝑻𝒉𝒎 (𝟏, 𝟐) (2 lines ⊥ 𝑎𝑛𝑑 ∥ 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑙𝑖𝑛𝑒 → 𝑙𝑖𝑛𝑒𝑠 ⊥ )
SWBAT: Write proofs involving Parallel and Perpendicular lines
OR
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Reasons Statements
1. 1. Given
2. p ∥ q 2. AIA’s ∥ (Converse of AIA Thm.)
3. ∡3 is a rt ∡ 3. ⊥ lines rt ∡s
3
4
4. ∡3 ≅ ∡4 4. ∥ CA’s
5. ∡4 is a rt ∡ 5. 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝑃𝑟𝑜𝑝 (4 𝑖𝑛𝑡𝑜 3)
6. s ⊥ p 6. rt ∡s ⊥ lines
SWBAT: Write proofs involving Parallel and Perpendicular lines
Exit Ticket
SWBAT: Write proofs involving Parallel and Perpendicular lines
SWBAT: Write proofs involving Parallel and Perpendicular lines
Reasons Statements
1.
1. given
2. ∡2 ∡10 2.
3. ∡5 ∡12 (A)
∡4 ∡11 (A)
3. ∥ AIA’s
4. ∡3 suppl. ∡4
∡10 suppl. ∡11
4. Linear Pair thm
5. ∡3 ∡10 5. Suppl. Thm
6. ∡2 ∡3 6. Trans. Prop (2, 5)
7. 𝐵𝐷 ≅ 𝐺𝐷 7.
8. 𝐺𝐷 ≅ 𝐶𝐹 (S) 8. Trans. Prop (1, 7)
9. DGE ≅FCE 9. ASA (3, 8, 3)
10. 𝐷𝐸 ≅ 𝐸𝐹 10. CPCTC
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