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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... Plane Geometry - Page 168by John Wesley Young, Albert John Schwartz - 1915 - 223 pagesFull view - About this book
| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...chord has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...general properties of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave **an angle of the one equal to an angle of the other and the** sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A = D (Jig.... | |
| Daniel Cresswell - 1819
...FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVU. 23. THEOREM. If two trapeziums **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two ^figures, about each of their angles, be proportionals, the remaining... | |
| Peter Nicholson - Building - 1823
...equal to the sum of the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which **have an angle of the one equal to an angle of the other,** are to each other as the rectangle of the sides about the equal Suppose* the two triangles joined,... | |
| Adrien Marie Legendre - 1825 - 224 pages
...: FH : : CD : HI ; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, **have an angle of the one equal to an angle of the other and the** sides about the equal angles proportional ; they are therefore similar (208). We might proceed in the... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which **have an angle of the one equal to an angle of the other and the** sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig. 122),... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...AC : FH : : CD : HI; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, **have an angle of the one equal to an angle of the other and the** sides about the equal angles proportional ; they are therefore similar (208). We might proceed in the... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the sides FG, GH, so that AB:FG::BC: GH. It follows from this, that the triangles ABC, FGH, having **an angle of the one equal to an angle of the other and the** sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF. These... | |
| Walter Henry Burton - Astronomy - 1828 - 68 pages
...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each **angle of the one equal to an angle of the other, and the** side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently... | |
| George Darley - 1828 - 169 pages
...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which **have an angle of the one equal to an angle of the other.** For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... | |
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