| Aaron Schuyler - Geometry - 1876 - 384 pages
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having **an angle of the one equal to an angle of the other,** and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB :... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other are to each other as the products** cf t he sides including the equal angles. Let the triangles ABC and ADE have the common angle A. We... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 = AC? + BI? + 4 ^ QED GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other are to each other as** tAe products of the sides including the equal angles. D. Let the triangles ABC and ADE have the common... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the **angle of the other are to each other as the products of the sides including the** supplementary angles. С \j 2. Show, geometrically, that the square described upon the sum of two straight... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the oiher are **to each other as the products of the sides including the equal angles.** Д Let the triangles ABС and ADE have the common angle A. Tjr , АABС ABX AС \\ e are to prove =... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral **angle of the other are to each other as the products of the** edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they **have an angle of the one equal to an angle of the other,** and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having **an angle of the one equal to an angle of the other,** and the including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А... | |
| J. G - 1878 - 408 pages
...secant contained between the point and the parallels. 14. // two parallelograms are equal in area, and **have an angle of the one equal to an angle of the other,** then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the... | |
| James McDowell - 1878 - 310 pages
...DEF are equiangular (constr.), therefore ABC and DEF are also equiangular. QED 81. If two triangles **have an angle of the one equal to an angle of the other,** and the rectangles under the sides about the equal angles equal, a side of each triangle being taken... | |
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