2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 4 Rombel 3
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Tugas Akhir Mata Kuliah Geometri Transformasi FMIPA Unnes Rombel 03 Kelompok 4 Meidila Wulandari (4101415007) Vita Fadillah (4101415021) Salma Maulidiyah (4101415036) Dewi Nova Y. (4101415066) Nurlaela Eka C. (4101415110) Info: fauzi1997@students.unnes.ac.id
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2018 Geometri Transformasi Perkalian 5 Isometri Kelompok 4 Rombel 3
- 2. ROMBEL 03 Dosen Pengampu : Drs. Suhito M.Pd. Disusun Oleh 1. Meidila Wulandari (4101415007) 2. Vita Fadillah (4101415021) 3. Salma Mauludiyah (4101415036) 4. Dewi Nova Yulianawati (4101415066) 5. Nurlaela Eka Cahyati (4101415110)
- 3. HASIL PERKALIAN 5 ISOMETRI DASAR 𝑴 𝒔 𝝄𝑹 𝑨,𝝋 𝟏 𝝄𝑮 𝑲𝑳 𝝄 𝑮 𝑷𝑸 𝝄𝑴 𝒕 𝝄𝑺 𝑩
- 5. Bayangan dari Bidang Segitiga UVW 𝑴 𝒔 𝝄 𝑹 𝑨,𝝋 𝟏 𝝄 𝑮 𝑲𝑳 𝝄 𝑮 𝑷𝑸 𝝄 𝑴 𝒕 𝝄 𝑺 𝑩Diketahui : 1. 𝑎 ⊥ 𝑡, 𝑎 ∕∕ 𝑏 , 𝑎 ∩ 𝑡 = 𝐵 2. Garis 𝑡 sebarang, 3. 𝑃𝑄 ⊥ 𝑏 4. 𝑃𝑄 ∕∕ 𝐾𝐿 5. 𝑏 ∕∕ 𝑐 ∕∕ d 6. 𝑑 ∩ 𝑒 = 𝐴 , 𝑚 ∠𝑒, 𝑑 = 1 2 𝜑1 7. Garis 𝑠 sebarang
- 6. BUKTI LANGSUNG 𝑀𝑠 𝜊𝑅 𝐴,𝜑 𝜊𝐺 𝐾𝐿 𝜊 𝐺 𝑃𝑄 𝜊𝑀𝑡 𝜊𝑆 𝐵 (∆𝑈𝑉𝑊) = 𝑀𝑠 𝜊𝑅 𝐴,𝜑 𝜊𝐺 𝐾𝐿 𝜊 𝐺 𝑃𝑄 𝜊𝑀𝑡 (∆𝑈1 𝑉1 𝑊1) = 𝑀𝑠 𝜊𝑅 𝐴,𝜑 𝜊𝐺 𝐾𝐿 (∆𝑈3 𝑉3 𝑊3) = 𝑀𝑠 𝜊𝑅 𝐴,𝜑 (∆𝑈4 𝑉4 𝑊4) = 𝑀𝑠 (∆𝑈5 𝑉5 𝑊5) = ∆𝑈6 𝑉6 𝑊6
- 10. Bayangan dari Bidang Segitiga UVW Oleh Diketahui : 1. 𝑎 ⊥ 𝑡, 𝑎 ∕∕ 𝑏 , 𝑎 ∩ 𝑡 = 𝐵 2. Garis 𝑡 sebarang, 3. 𝑃𝑄 ⊥ 𝑏 4. 𝑃𝑄 ∕∕ 𝐾𝐿 5. 𝑏 ∕∕ 𝑐 ∕∕ d 6. 𝑑 ∩ 𝑒 = 𝐴 , 𝑚 ∠𝑒, 𝑑 = 1 2 𝜑1 7. Garis 𝑠 sebarang Akan ditunjukan bahwa : 𝑀𝑠 𝜊𝑅 𝐴,𝜑1 𝜊𝐺 𝐾𝐿 𝜊 𝐺 𝑃𝑄 𝜊𝑀𝑡 𝜊𝑆 𝐵 △ 𝑋𝑌𝑍 = 𝑅 𝐹,𝜑4 (∆𝑈𝑉𝑊)
- 11. BuktiTak Langsung 𝑀𝑠 𝜊𝑅 𝐴,𝜑1 𝜊𝐺 𝐾𝐿 𝜊 𝐺 𝑃𝑄 𝜊𝑀𝑡 𝜊𝑆 𝐵 = 𝑀𝑠 𝜊 𝑀𝑒 𝜊𝑀 𝑑 𝜊 𝑀 𝑑 𝜊𝑀𝑐 𝜊 𝑀𝑐 𝜊𝑀 𝑏 𝜊𝑀𝑡 ο 𝑀𝑡 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊𝑀𝑒 𝜊 𝑀 𝑑 𝜊𝑀 𝑑 𝜊 𝑀𝑐 𝜊𝑀𝑐 𝜊𝑀 𝑏 𝜊 𝑀𝑡 𝜊𝑀𝑡 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊𝑀𝑒 𝜊 𝐼 𝜊 𝐼 𝜊 𝑀 𝑏 𝜊 𝐼 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊𝑀𝑒 𝜊 𝑀 𝑏 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊 𝑅 𝐶,𝜑2 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊 𝑀𝑙 𝜊𝑀 𝑘 𝜊𝑀 𝑎 = 𝑀𝑠 𝜊𝑀𝑙 𝜊(𝑀 𝑘 𝜊𝑀 𝑎) = 𝑀𝑠 𝜊 𝑀𝑙 𝜊𝑆 𝐷 = 𝑀𝑠 𝜊 𝑀𝑙 𝜊𝑆 𝐷 = 𝑀𝑠 𝜊 𝐺 𝑋𝑌 𝜊𝑀𝑟 = 𝑀𝑠 𝜊[ 𝑀𝑙 𝜊𝑀 𝑢 𝜊𝑀𝑟] = (𝑀𝑠 𝜊 𝑀𝑙) 𝜊 ( 𝑀 𝑢 𝜊𝑀𝑟) = 𝑅 𝐸,𝜑3 𝜊 𝑆 𝐷 = (𝑀 𝑢 𝜊𝑀𝑧) 𝜊 ( 𝑀𝑧 𝜊𝑀 𝑤) = 𝑀 𝑢 𝜊 𝐼 𝜊𝑀 𝑤 = 𝑀 𝑢 𝜊𝑀 𝑤 = 𝑅 𝐹,𝜑4
- 12. Syarat pada BuktiTak Langsung ■ 𝑎 ⊥ 𝑡, 𝑎 ∕∕ 𝑏 , 𝑎 ∩ 𝑡 = 𝐵 ■ Garis t sembarang, ■ 𝑃𝑄 ⊥ 𝑏 ■ 𝑃𝑄 ∕∕ 𝐾𝐿 ■ 𝑏 ∕∕ 𝑐 ∕∕ d ■ 𝑑 ∩ 𝑒 = 𝐴 , 𝑚 ∠𝑒, 𝑑 = 1 2 𝜑1 ■ Garis s sembarang 5. 𝑙 ∕∕ 𝑢, 𝑢 ⊥ 𝑟 𝑋𝑌 ⊥ 𝑙, 𝑑𝑙,𝑢 = 1 2 𝑋𝑌 2. 𝑒 ∩ 𝑏 = 𝐶 , 𝑚 ∠𝑏, 𝑒 = 1 2 𝜑2 3. 𝑙 ∩ 𝑘 = 𝐶 , 𝑚 ∠𝑘, 𝑙 = 1 2 𝜑2 4. 𝑘 ⊥ 𝑎, k ∩ 𝑎 = 𝐷 6. 𝑠 ∩ 𝑙 = 𝐸 , 𝑚 ∠𝑙, 𝑠 = 1 2 𝜑3 7. u ⊥ 𝑟, u ∩ 𝑟 = 𝐷 8. 𝑢 ∩ 𝑧 = 𝐸 , 𝑚 ∠𝑧, 𝑢 = 1 2 𝜑3 𝑧 ⊥ 𝑤, z ∩ 𝑤 = 𝐷 9. 𝑢 ∩ 𝑤 = 𝐹 , 𝑚 ∠𝑤, 𝑢 = 1 2 𝜑4 1.
- 16. TERIMA KASIH