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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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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...two angles of the other ( 236). When their homologous sides are proportional ( 240). When they have an angle of one equal to an angle of the other, and the sides including these angles proportional ( 242). When their sides are parallel each to each,...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 208 pages
...of the tests of similarity is satisfied. PROP. XV. THEOREM 242. Two triangles are similar when they have an angle of one equal to an angle of the other, and the sides including these angles proportional. Draw A ABC and A'B'C' having ZA = ZA', and the sides...
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First Course in Algebra: With Eight Thousand Examples Including Three ...

Albert Harry Wheeler - Algebra - 1908 - 698 pages
...taken parallel to the axis of Y, and accordingly the triangles OfiA and OH' A' are similar, since they have an angle of one equal to an angle of the other, and the included sides proportional. It follows that either of the points A or A' lies on the straight...
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Annual Report, Volumes 2-3

Civil Service Commission of Canada - Civil service - 1910 - 238 pages
...triangles BDE, ADC are equal in area. 9. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional. Describe an isosceles triangle equal in area to a given triangle and having its vertical angle equal...
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Exercises in Geometry

Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...bisector of the opposite angle. Group V. Similar Polygons 1. Two parallelograms are similar if they have an angle of one equal to an angle of the other, and the including sides proportional. 2. Two rectangles are similar if two adjacent sides of one are...
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Plane Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Plane - 1909 - 204 pages
...have the same ratio as the squares oftheir corresponding sides. 292. Co R. 2. // two triangles that have an angle of one equal to an angle of the other are equivalent, the product of the sides including the angle in one equals the product of the sides...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...perpendicular to the sides of the other are similar. PLANE GEOMETRY. 259. THEOREM. // two triangles have an angle of one equal to an angle of the other and the pairs of adjacent sides in the same ratio, the triangles are similar. \ o' (Why?) V BC Given...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...respectively parallel or perpendicular to the sides of the other are similar. 259. THEOEEM. // two triangles have an angle of one equal to an angle of the other and the pairs of adjacent sides in the same ratio, the triangles are similar. B' C' c Given A ABC and...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...whose bases are 6 and 6' and whose other sides are each equal to s. PROPOSITION VIII. THEOREM 49R 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 the equal angles. 4 GCD 2. 3. To prove Given...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...tangent is a mean proportional between the whole secant and its external segment. 4. 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. 6. Two triangles ABC and ABC...
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