 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...sides, and parallel to them, will be equal. 10. To construct a square, having a given diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...the perinieters of similar polygons are to one another, etc, THEOREM XXIII. Two triangles which have an angle in the one equal to an angle in the other, are to each other as the rectangle of the sides about the equal angles. Let ABC and def be two triangles having the angles A... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...hypothenuse B C. PBOPOSITION XXVIII. — THEOREM. 272. Two triangles, having an angle in each equal, are to each other as the rectangles of the sides which contain the equal angles. A Let the two triangles ABC, ADB have the angle A in common ; then will the triangle ABC be to the... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...identical (th. 5, BI), which is absurd, since their angles are unequal. THEOREM vrn. Triangles which have an angle in the one equal to an angle in the other, and the sides about these angles proportional, are equiangular. Let ABC, DEF, be two triangles, having... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...sides, and parallel to them, will be equal 10. To construct a square, having a given diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...similar, the angles EA B and tab are equal, and EA : AB : : ea : ab. Hence the two triangles, EAB and eab, having an angle In the one equal to an angle in the other, and the sidea about these angles proportional, are equiangular and similar, and the angles ABE and... | |
 | Euclid - 1868 - 138 pages
...oiher, have their sides about the equal angles reciprocally proportional ; and triangles which have an angle in the one equal to an angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another. PART I.... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...hypothenuse B C. PROPOSITION XXVIII. — THEOREM. 272. Two triangles, having an angle in each equal, are to each other as the rectangles of the sides which...A in common ; then will the triangle ABC be to the tri- $>/ angle AD.E as AB X AC to AD X AE. Join BE ; then the triangles ABE, BC ADE, having the common... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...varied at pleasure, without altering the lengths of the sides. THEOREM XVII. If two triangles have an angle in the one equal to an angle in the other, and the sides containing these angles proportionul,the \wo triangles will be equiangular and similar.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...segments of the base (59) are AE and CJEL (I. 17.) (1. 45.) (16.) 61 1 Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC: ADE—ABX AC: ADX AE Draw BE. (13.) (Pn. 24.) (Pn. 21.) 62. Prove... | |
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Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus the triangle ABC (fig. 
