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If BC || DE, and angle AEF is a right angle, then is AC > AB?

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If BC || DE, and angle AEF is a right angle, then is AC > AB? [#permalink] New post  17 Dec 2019, 09:54
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If BC || DE, and angle AEF is a right angle, then is AC > AB?

(1) DE = EF

(2) AE > AD

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Re: If BC || DE, and angle AEF is a right angle, then is AC > AB? [#permalink] New post  18 Dec 2019, 04:13
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the question is asking: is AC > AB?
since BC || DE, rephrases for the question can be:
is AE > AD?
is ∠ADE > ∠AED
is ∠ABC > ∠ACB

From statement (1), ∠EDF = ∠EFA = ∠CBD
∠AEF = 90, so ∠DEF<90
∠DEF = 180-2(∠EDF) < 90
45 < ∠EDF
so 45 < ∠CBD and ∠ABC > 135 --> so ∠ACB < 135 -- > ∠ABC > ∠ACB --> sufficient

From statement (2), it clearly says that AE > AD,
so AC > AB because we have two similar triangles ABC and ADE --> sufficient

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Re: If BC || DE, and angle AEF is a right angle, then is AC > AB? [#permalink]
18 Dec 2019, 04:13
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