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The Encyclopedia of Geometry (0030)
Problem Two triangles, in which the three corresponding sides are equal respectively, are congruent. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution In $△ABC$ and $△DEF$, $$AB=DE, \quad BC=EF \quad and \quad AC=DF.$$…
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Koh-jingu Shrine (1880), Higashiaso, Soja City, Okayama Prefecture (04)
Problem If there is a cone, its generating line is $a$, and the slope angle is $α$, find the area of the side surface. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution The…
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The Encyclopedia of Geometry (0029)
Problem Two triangles, in which a pair of corresponding sides and angles at both ends of them are respectively equal, are congruent. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Now, if we…
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The Encyclopedia of Geometry (0028)
Problem Two triangles in which a pair of corresponding sides and the included angle are equal are congruent. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Now, if we put $A$ on…
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The Encyclopedia of Geometry (0027)
Problem When two line segments $AB$ and $CD$ are parallel to each other in the same direction, if we take a point $P$ that is not between $AB$ and $CD$, then $$|∠ABP-∠CDP|=∠BPD.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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The Encyclopedia of Geometry (0026)
Problem Suppose that two line segments $AB$ and $CD$ are parallel to each other in the same direction. Then, if the point $P$ is between $AB$ and $CD$, $$∠ABP+∠CDP=∠BPD.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…
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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 $$∠ABC+∠DEF=2∠R.$$ $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…