Question by Kantai Collection - Discuss with MathYouLike

Kantai Collection

19/07/2017 at 15:02

Give rectangle ABCD , connect C to any point E on the BD diagonal , on ray EC , choose F so that EF = EC. Draw FH and FK perpendicular to AB and AD . Prove that :

a) Quadrilateral AHFK is a rectangle

b) AF parellel to BD and KH parellel to AC

c) Three points E,H,K are straight .

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ღ kekio ღ 21/07/2017 at 08:30

a, consider the triangle AHFK: \(\widehat{A}=\widehat{H}=\widehat{K}=90^o\)

should AHFK is rectangle

b, consider the triangle ACF :OA=OC;EC=EF

should OE is the average line of the triangle ACF

should OE//AF or AF//BD

similar: the average line is EJ triangle ACF
should EJ//AC

similar: the average line is EJ triangle ACF
should EJ//AC

\(\Rightarrow\widehat{AKJ}=\widehat{KAJ}+\widehat{KAJ}=\widehat{KDE}\)pairs of isotopes

\(\Rightarrow\widehat{AKJ}=\widehat{KDE}\) or KDE loss triangle

inferred :\(\widehat{JK}=\widehat{DEK}=\dfrac{180-KDE}{2}\) should K; J and E line
that K; J; H line
should K; H and E also in line and HK//AC
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ღ kekio ღ 21/07/2017 at 08:06

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