 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...GEOMETRY.—BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplo mcnt of an angle of the other are to each other as the products of the siiitM including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described... | |
 | 1876 - 646 pages
...Define similar polygons. Prove that two triangles are similar when they are mutually equiangular. 2. Two triangles having an angle of the one equal to...products of the sides including the equal angles. 3. To inscribe A circle in a given triangle. 4. The side of a regular inscribed hexagon is equal to... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...sides, nor does 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 :... | |
 | Richard Wormell - 1876 - 268 pages
...demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...-ЦТ? + Ш? = 4 2 + 4 2 + 4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to...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
...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 - 416 pages
...A'B' '" WC'' A'B' 145 But Since AE EH AE B'G'' = A'B', § 278 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 In the triangles ABC and A' B' C' let . . , ..... | |
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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. 
