#Trigonometry "prove that..." help

20 messages · Page 1 of 1 (latest)

thick haven
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Well, I have to prove that ABD = ABF.
Infos are: ABC is a right triangle, BCD is an equilateral, FD is the height of BCD,
I've been trying to solve this for 2 days and I feel that it's not that hard but I just cant.

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north juniperBOT
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vestal vault
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What do you have to prove

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What do you mean with ABD = ABF

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The angles?

stray radish
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yeah

thick haven
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that they have same area

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sorry for not specifying

stray radish
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oh

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F must be the midpoint of BC

thick haven
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it is

tawny rune
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then maybe start by letting BF = 1

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your goal is to prove the area of ABD is equal to the area of ABF

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you can use half times base times height formula for triangle ABF and area of triangle formula using trig (half times a times b times sinC) for triangle ABD

lapis fulcrum
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if you let AB be the base of the triangle

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you just need to show that they have the same height

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this is true because, dropping a perpendicular from D to AB and naming it X, you get that BXDF is a rectangle