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The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw...
Elements of Plane Geometry: For the Use of Schools - Page 71
by Nicholas Tillinghast - 1844 - 96 pages

The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 250 pages
...case an isosceles triangle with two given lines in the plane ? (1893.) 14. Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles, prove that the bisector...

Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 228 pages
...and tangent to a given line at a given point B, and prove the construction correct. 5. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including those angles. (B) 1. The shadow cast on level...

Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...and tangent to a given line at a given point B, and prove the construction correct. 5. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including those angles. (В) 1. The shadow cast on level...

Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...Compare area of AliE, BEFand. FEC, EDC. PROPOSITION VII. THEOREM. 261. The areas of two triangles having an angle of the one equal to an angle of the other, are to each other as the products of the sides including the equal angles. . Let ABC and ADE be two...

Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...of a trapezoid is equal to half the sum of its bases multiplied by the altitude. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 412. The areas of two similar...

Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 276 pages
...from the other vertices of the polygon. AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Let the triangles ABC and...

Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...the other vertices of the polygon. 190 AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Let the triangles ABC and...

Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...equal, respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 357. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. A' In the triangles ABC and A'B'C', let ZA = Z A',...