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" Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages
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Junior High School Mathematics ...

Edson Homer Taylor, Fiske Allen - Mathematics - 1923 - 104 pages
...angles of the other, the triangles are similar. THEOREM XLVII 197. Two triangles are similar if they have an angle of one equal to an angle of the other and the including sides proportional, c c> A '" B A' B' 198. Analysis. Given A ABC and A A'B'C' having...
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Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...FUNDAMENTAL THEOREMS BOOK III Proposition 4. Angle and Proportional Sides 213. Theorem. If two triangles have an angle of one equal to an angle of the other and the including sides proportional, the triangles are similar. •BA Given the AABC and A'B'C' with...
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Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...triangle are equal respectively to two angles of another, the triangles are similar. 4. If two triangles have an angle of one equal to an angle of the other and the including sides proportional, the triangles are similar. 5. If two triangles have their sides...
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The Teaching of Mathematics in the Elementary and the Secondary School

Jacob William Albert Young - Mathematics - 1924 - 451 pages
...similar if (a) they have two angles of one equal, respectively, to two angles of the other; (b) they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 14. If two...
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Abraham Lincoln: The Prairie Years, Volume 1

Carl Sandburg - Presidents - 1926 - 528 pages
...centres or circumferences," and "Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and parallelograms which have one angle of the one equal to one angle of the other, and their sides about...
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Abraham Lincoln: The Prairie Years,

Carl Sandburg - 1926 - 528 pages
...centres or circumferences," and "Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and parallelograms which have one angle of the one equal to one angle of the other, and their sides about...
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The Reorganization of Mathematics in Secondary Education (part I): A ..., Part 1

National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...similar if (a) they have two angles of one equal, respectively, to two angles of the other; (6) they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. [59*, 60*,...
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Information Relative to the Appointment and Admission of Cadets to the ...

Military Academy, West Point - 1934 - 964 pages
...center of a circle and a tangent, if one of the intercepted ares is 41. 10 Prove that the areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including those angles. 10 Construct a triangle equivalent...
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Official Register of the Officers and Cadets

United States Military Academy - 1942 - 1020 pages
...center of a circle and a tangent, if one of the intercepted arcs is 41. 10 Prove that the areas of two triangles which have an angle of one equal to an angle of the other arc to each other as the products of the sides including those angles. 10 Construct a triangle equivalent...
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Annual Report of the Department of Education to the General Assembly of the ...

Georgia. Department of Education - Education - 1919 - 648 pages
...square of the hypotenuse is1 equal to the sum of the squares of the legs. Demonstrate: If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Demonstrate:...
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