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" 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. "
Elements of Plane and Solid Geometry - Page 188
by George Albert Wentworth - 1877 - 398 pages
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...similarity of ABC and A'B'C', BC AB hence A'D and we have _. B'c' 373-- EXERCISE. ^ *• (/ Theorem.—Two triangles having an angle of the one equal to an angle...products of the sides including the equal angles. Suggestion. Let ADE and ABC be the two triangles. Draw BE, and compare the two triangles with AEB....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...(v. V., Exercise 16.) 4. Two tetraedrons which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles, (v. IV., 19, Exercise.) .—•> o Suggestion. The intersections...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1888 - 978 pages
...other. 3. The volumes of two tetrahedrons having a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the three edges of these trihedral" angles. 4. A sphere may be inscribed in any given tetrahedron. 5. In...
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Calendar of Dalhousie College and University

Dalhousie University - 1888 - 212 pages
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles have an angle of the one equal to an angle of the other, their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of...
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A Text-book of Geometry

George Albert Wentworth - Geometry, Analytic - 1889 - 264 pages
...ADE AD X AE §370 * Ex. 292. The areas of two triangles which have an angle of the one supplementary to an angle of the other are to each other as the products of the sides including the supplementary angles. /, > . \- ' ' PLANE GEOMETRY. — BOOK IV. COMPARISON OF POLYGONS. PROPOSITION...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...radius of the circle. COMPARISON OF AREAS. 187. Theorem. The areas of two triangles having an angle of one equal to an angle of the other are to each other as the rectangles of the sides including the equal angles. 188. Theorem. Similar triangles are to each other...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...altitudes. 397. // 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. 398. The areas of any two similar triangles are to each other as the squares of any two homologous...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...THEOREM 39 7 . 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. Given the A ABC and ADF having1 /.A inocommon/ _ A ABC_ABXAO To prove A~TD^~ ADXAF' Proof, Draw the...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...THEOBEM 397. 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. A Given the A ABC and ADF having ZA in common/ _, A ABC ABXAC T°prOVe ~K~ADF'= ADXAF Proof. Draw the...
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