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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 $$∠ABC=∠DEF.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0021)
Problem When there are two straight lines that intersect on the same plane, two straight lines that are parallel to each of them will always intersect. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0020)
Problem The two straight lines $EF$ and $GH$, which are perpendicular to the two parallel lines $AB$ and $CD$, respectively, are parallel to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…
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The Encyclopedia of Geometry (0019)
Problem When a straight line $XY$ is perpendicular to $CD$ of the parallel lines $AB$ and $CD$, it is also perpendicular to the other $AB$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…
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The Encyclopedia of Geometry (0018)
Problem Two straight lines perpendicular to the same straight line are parallel to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Assume that $AB$ and $CD$ are both orthogonal to $XY$…
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Koh-jingu Shrine (1880), Higashiaso, Soja City, Okayama Prefecture (01)
Koh-jingu Shrine is located $1.8 \ km$ north of Ashimori Station on the JR Kibi Line. Problem If the distance of $1°$ at the equator is $28.03 \ ri$, how much is the distance of $1°$ at $35°$ north latitude? ($1 \ ri$ is approximately $3.927 \ km$.) $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$…
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The Encyclopedia of Geometry (0017)
Problem When three straight lines $a, b$ and $c$ are on the same plane, and $a∥b$ and $a∥c$, then $$b∥c.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Assuming $b∦c$, two straight lines…
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The Encyclopedia of Geometry (0016)
Problem When two parallel lines intersect with a straight line, the corresponding angles or alternate angles are equal, and the interior angles (or the exterior angles) on the same side are complementary to each other. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0015)
Problem Two straight lines are parallel when they intersect with a straight line and alternate angles they form are equal. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Let the two straight lines…