Pada kesempatan ini admin Rumus Matematika akan berbagi informasi mengenai Kedudukan Garis Terhadap Garis dan Bidang Ruang Dimensi Tiga yang merupakan bagian materi Matematika SMA Kelas 10. Sebelumnya admin juga sudah berbagi tentang Kedudukan Titik Terhadap Garis dan Bidang Ruang Dimensi Tiga.
Sebagai ilustrasi sekarang perhatikan gambar di bawah ini.
Gambar
di atas merupakan gambar tiang kabel listrik, jika kabel listrik
tersebut kita anggap sebagai garis. Bagaimanakah letak atau kedudukan
kabel dengan kabel lainnya?
Kedudukan Garis Terhadap Garis
Konsep
ini sudah Anda pelajari pada saat Anda duduk di bangku SMP/MTs. Untuk
itu Mafia Online tidak akan membahasnya di sini, akan tetapi untuk
melengkapi materi SMP/MTs tentang kedudukan garis dengan garis pada
postingan ini akan ditambahkan tentang aksioma dua garis sejajar dan
contoh soalnya.
Aksioma/Postulat Dua Garis Sejajar
Melalui sebuah titik yang berada di luar sebuah garis, hanya dibuat sebuah garis yang sejajar dengan garis itu.
Silahkan
perhatikan dan dipelajari contoh soal di bawah ini untuk memantapkan
pemahaman Anda tentang konsep kedudukan garis terhadap garis.
Kedudukan Dua Buah Bidang Ruang Dimensi Tiga
Sekarang perhatikan gambar di bawah ini.
Gambar
di atas merupakan gambar sebuah lorong di suatu sekolah. Lorong
tersebut diapit oleh dua buah dinding. Bagaimana kedudukan kedua dinding
tersebut? Untuk menjawab pertanyaan tersebut Anda harus paham dengan
konsep kedudukan bidang terhadap bidang lainnya. Kedudukan bidang
terhadap bidang lain ada tiga kemungkinan, yaitu berimpit, sejajar, dan
berpotongan.
Dua Bidang Berimpit
Dua bidang dikatakan berimpit, jika setiap titik terletak pada kedua bidang, seperti gambar di bawah ini.
Dua Bidang Sejajar
Dua
bidang dikatakan sejajar, jika kedua bidang tersebut tidak mempunyai
satu pun titik persekutuan, seperti gambar di bawah ini.
Dua Bidang Berpotongan
Dua bidang dikatakan berpotongan, jika kedua bidang tersebut mempunyai sebuah garis persekutuan, seperti gambar di bawah ini.
Untuk memantapkan pemahaman Anda tentang kedudukan bidang dengan bidang lainnya, silahkan perhatikan contoh soal berikut ini.
Contoh Soal Kedudukan Dua Buah Bidang Ruang Dimensi Tiga
1. Perhatikan kubus ABCD.EFGH pada gambar di bawah ini.
a) Sebutkan tiga pasang bidang yang sejajar.
b) Sebutkan dua pasang bidang yang berpotongan.
Penyelesaian:
a) Bidang ABCD sejajar dengan bidang EFGH, bidang ABFE sejajar dengan bidang CDHG, dan BCGF sejajar dengan bidang ADHE.
b) Bidang ABGH berpotongan dengan bidang CDEF dan bidang BCHE berpotongan dengan bidang ADGF.
2. Perhatikan kubus di bawah ini.
Bidang sisi CDHG sebagai wakil bidang u. Tentukan bidang sisi kubus yang:
a. berimpit dengan bidang u
b. sejajar dengan bidang u
c. berpotongan dengan bidang u
Penyelesaian:
Bidang sisi kubus yang:
a. berimpit dengan bidang u adalah sisi CDHG
b. sejajar dengan bidang u adalah ABFE
c. berpotongan dengan bidang u adalah ABCD.
eperti kita ketahui
bahwa pada setiap bangun datar terdapat sifat ataupun ciri yang menjadi
cirikhas dari bangun datar tersebut. Diantara sifat-sifat tersebut ada yang
dinakaman dengan simetri. Nah, untuk materi kali ini yang akan dibahas adalah
mengenai macam-macam simetri pada bangun datar. Materi ini tidak terlalu sulit
untuk dipahami karena kita hanya perlu menggunakan logika pemikiran untuk
mengerti tentang simetri apa saja yang ada atau dimiliki oleh sebuah bangun
datar. Saya kira tidak perlu berlama-lama lagi mari kita simak langsung
penjelasan materinya di bawah ini:
Penjelasan Pengertian Macam-macam Simetri pada Bangun Datar Lengkap
Simetri Lipat
Secara singkat simetri lipat pada bangun datar bisa
didefinisikan sebagai banyaknya lipatan pada bangun datar yang bisa membagi
bangun datar tersebut sehingga setengah bagian dari bangun datar tersebut bisa
menutupi setengah bagian yang lain. Garis yang dapat membagi sebuah bangun
datar menjadi dua dan kongruen disebut sebagai sumbu simetri. Perlu kalian
ketahui bahwasannya tidak setiap bangun datar memiliki garis yang dinamakan
sebagai sumbu simetri. Ada beberapa bangun datar yang tidak memiliki sumbu simetri
sama sekali. Kalian bisa melihat beberapa bangun datar yang memiliki sumbu
simetri pada gambar berikut.
Pada gambar di atas garis atau sumbu simetri
digambarkan dengan garis putus-putus. Apabila
kita melipat atau memotong sebuah bangun datar dengan mengikuti garis-garis
simetri tersebut maka bangun datar itu akan terbagi menjadi dua bagian yang
sama besar.
Sebelumnya telah di bahas tentang
rumus luas dan keliling layang-layang. Sekarang kita lanjutkan lagi materi
mengenai bangun datar dan kali ini yang akan dibahas adalah tentang rumus luas
dan keliling dari bangun datar trapesium. Trapesium adalah sebuah bangun datar
yang dibentuk dari empat buah rusuk dimana dua diantara rusuk tersebut
posisinya sejajar tapi tidak sama panjangnya. Trapesium termasuk kedalam
kelompok bangun datar berjenis segi empat. Trapesium sendiri terbagi ke dalam
tiga jenis yaitu trapesium sembarang (keempat rusuknya tidak sama panjang),
trapesium sama kaki (sepasang rusuk sama panjang dan sepasang rusuk sejajar)
serta trapesium siku-siku (keempat sudutnya siku-siku). Ketiga jenis trapesium
tersebut dapat anda lihat pada gambar berikut ini:
Rumus matematika kali ini
khusus akan membahas beragam jenis rumus yang biasa digunakan untuk
menyelesaikan soal-soal yang berkaitan dengan trapesium. Rumus yang biasa
digunakan adalah rumus untuk mencari luas dan keliling dari sebuah trapesium. Berikut
ini adalah penjelasan mengenai rumus luas dan keliling trapesium lengkap dengan
contoh soal besera pembahasannya. Yuk, mari kita pelajari bersama.
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