 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C'...  The Elements of Geometry - Page 148by Henry W. Keigwin - 1897 - 227 pagesFull view - About this book
 | 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... | |
 | George Albert Wentworth - 1889 - 276 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... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...median. Proposition VII. A Theorem. 242. The areas of two triangles having an angle in each equal are to each other as the products of the sides including the equal angle. Proposition VIII. A Theorem. 243. The square described on the sum of two lines is equal to the... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...about 300 BC (Prop. 47, Book I. Euclid). Proposition 8. Theorem. 375. The areas of two triangles having an angle of the one equal to an angle of the other,...products of the sides including the equal angles. Hyp. Let ABC, ADE be the two A s A having the common Z A. A ABC AB X AC ~ To prove — T^T; = T^F;... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...Proposition 2 1 . Theorem.* 637. Two tetraedrons which have a triedrul angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of these triedral angles. Hyp. Let S-ABC, S-DEF be the two given tetraedrons, having the... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...X AE §370 QE r'. 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 0' the sides including the supplementary angles. COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM.... | |
 | Examinations - 1893 - 408 pages
...that an angle formed by a tangent and a chord is measured by one half the intercepted arc. 1 2 5 Prove that the areas of two triangles which have an angle...products of the sides including the equal angles. 16 6 Prove that the area of a regular polygon is equal to half the product of its perimeter and apothem.... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...GEOMETRY. 159. THEOREM. Two triangular pyramids 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 including the equal triedral angles. C' Place the equal triedral angles in coincidence at 0.... | |
 | William Chauvenet - 1893 - 340 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.) Suggestion. The intersections of... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...segments of one is equal to the product of the segments of the other. 5. Two triangles having an angle of one equal to an angle of the other are to each other as the product of the sides including the equal angles. 6. Construct a polygon similar to a given polygon... | |
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