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Koh-jingu Shrine (1880), Higashiaso, Soja City, Okayama Prefecture (03)
Problem If a person’s moon shadow is reflected in the water, its length is $10 ft$ from the feet, and the height from the water’s surface to the eyes is $6 ft$, How many degrees does the moon hang over? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0025)
Problem If the two sides $AB$ and $AC$ of $∠BAC$ are, respectively, parallel to the two sides $DE$ and $DF$ of $∠EDF$, then the bisector $AM$ of the former angle and the bisector $DN$ of the latter are parallel or perpendicular to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$…
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The Encyclopedia of Geometry (0024)
Problem When a straight line $EF$ cuts across parallel lines $AB$ and $CD$, the bisectors of the alternate angles and the corresponding angles are parallel. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…
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The Encyclopedia of Geometry (0023)
Problem For $∠ABC$ and $∠DEF$, if the sides $AB$ and $DE$ are parallel in the same direction, and $BC$ and $EF$ are parallel in opposite direction, then $$∠ABC+∠DEF=2∠R.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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Koh-jingu Shrine (1880), Higashiaso, Soja City, Okayama Prefecture (02)
Problem If the distance of $1°$ at the equator is $28.03 \ ri$, how many degrees north latitude is the place where the distance of $1°$ is $27 \ ri$ ? ($1 \ ri$ is approximately $3.927 \ km$.) $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0022)
Problem When the two sides $AB$ and $BC$ of $∠ABC$ are, respectively, parallel to the two sides $DE$ and $EF$ of $∠DEF$ in the same direction or in the opposite direction, then $$∠ABC=∠DEF.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0021)
Problem When there are two straight lines that intersect on the same plane, two straight lines that are parallel to each of them will always intersect. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0020)
Problem The two straight lines $EF$ and $GH$, which are perpendicular to the two parallel lines $AB$ and $CD$, respectively, are parallel to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…
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The Encyclopedia of Geometry (0019)
Problem When a straight line $XY$ is perpendicular to $CD$ of the parallel lines $AB$ and $CD$, it is also perpendicular to the other $AB$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…
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The Encyclopedia of Geometry (0018)
Problem Two straight lines perpendicular to the same straight line are parallel to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Assume that $AB$ and $CD$ are both orthogonal to $XY$…