 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 and Solid Geometry - Page 146by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles.... | |
 | J. G - 1878 - 408 pages
...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 Maurice Wilson - 1878 - 450 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...their third angles are both acute, or both obtuse, the triangles are similar. Compare I. 96 - 100. 116. 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 (Fig.... | |
 | District of Columbia. Board of Education - Education - 1881 - 314 pages
...plant analysis. TENTH GRADE. MAY itf. GEOMETRY AND TRIGONOMETRY. (Twenty credits.) 1. Theorem: — Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. 2. If from the diagonal BD of a square ABCD,... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...to the sum of the squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 3-41. Two triangles having an angle of the one equal to an angle of the other are to each other an the products of the sides including the equal angles. Let the triangles ABC and... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...proportional, and the figures are noi similar. il A'B' '' WC'' § 278 . AE A'B' Ax. 1 EH B'C'' Since AE = A'B', Cons. PROPOSITION VI. THEOREM. ' 284. Two triangles...similar. A A' In the triangles ABC and A' B' C' let ZA=ZA', and — = — . A' B' A' C" We are to prove AABC and A' B' C" similar. Apply the A A' B' C"... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...the figures are not similar. But Since AB A'B' WC ~ B'C'' . AE A'B' EH B'С'' AE = A'B', Hyp. Ax. 1 PROPOSITION VI. THEOREM. 284. Two triangles having...and the including sides proportional, are similar. A In the triangles ABC and A' B' С' let /A y », , AB AC Z. A — /. A', and = A'B' A'C' We are to prove... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...ratio of AN to NB is the duplicate of the ratio of AM to MB. 2. If two triangles of equal area have an angle of the one equal to an angle of the other, prove that the sides about the equal angles are reciprocally proportional. 3. Shew how to divide a... | |
 | Mathematical association - 1883 - 86 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
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