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Perhatikan gambar! Buktikan !

Pertanyaan

Perhatikan gambar!

Buktikan triangle A B E tilde triangle B C D!

Pembahasan Soal:

Dua segitiga sebangun jika sudut yang bersesuaian serta sisi yang bersesuaian sebanding

Pembuktian sisi yang sebanding

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell A E space colon space C D ? end cell row cell fraction numerator A E over denominator C D end fraction end cell equals cell fraction numerator 70 divided by 10 over denominator 40 divided by 10 end fraction end cell row blank equals cell 7 over 4 end cell row blank blank cell B E space colon space B D ? end cell row cell fraction numerator B E over denominator B D end fraction end cell equals cell fraction numerator 112 divided by 16 over denominator 64 divided by 16 end fraction end cell row blank equals cell 7 over 4 end cell row blank blank cell A B space colon space B C ? end cell row cell A B end cell equals cell square root of B E squared minus A E squared end root end cell row blank equals cell square root of 112 squared minus 70 squared end root end cell row blank equals cell square root of 12.544 minus 4.900 end root end cell row blank equals cell square root of 7.644 end root end cell row blank equals cell 87 comma 429972 end cell row blank equals cell 87 comma 4 space cm end cell row cell B C end cell equals cell square root of B D to the power of italic 2 italic minus C D to the power of italic 2 end root end cell row blank italic equals cell square root of 64 squared minus 40 squared end root end cell row blank equals cell square root of 4.096 minus 1.600 end root end cell row blank equals cell square root of 2.496 end root end cell row blank equals cell 49 comma 959984 end cell row blank equals cell 50 space cm end cell row cell fraction numerator A B over denominator B C end fraction end cell equals cell fraction numerator 87 comma 4 divided by 12 comma 4 over denominator 50 divided by 12 comma 4 end fraction end cell row blank equals cell 7 over 4 end cell end table

Dari pembuktian di atas terbukti bahwa sisi-sisi segitiga sebanding,

Jadi, triangle A B E tilde triangle B C D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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