| William Guy Peck - Conic sections - 1876 - 412 pages
...quan• tity ^p, and reducing, we have ACD : PQR :: CD2 : QR2. But, CD2:QR2::DA2:RP2::AC2:PQ2. c Hence, **two similar triangles are to each other as the squares of any two homologous** sides. Cor. 2. If ACD and PQR are similar, ACD and EFD are also similar; consequently the second couplets... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...similar triangles, homologous altitudes are to each other as any pair of homologous sides. XXVI. Theorem. **The areas of two similar triangles are to each other as the squares** of two homologous sides or altitudes. abc. ABC : abc = HYPOTH. A ABC ~ To IJE PROVED. AB2 : a&2. PROOF.... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and C to F : then the **triangles are to each other as the squares of any two homologous** sides. Because the angles A and D are equal, we have (P. XXTV.), ABC : DEF : : ABxAC : DE x DF ; and,... | |
| Webster Wells - Geometry - 1886 - 392 pages
...hence, CD AB C'D' A'B' Substituting in (1), we have ABC = A'B'C' A'B AB AB A'B' AB2 335. SCHOLIUM. **Two similar triangles are to each other as the squares of any two homologous** lines. PROPOSITION VIII. THEOREM. 336. Two triangles having an angle of one equal to an angle of the... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...equalities, AABC_ABxAC AADE ADxAE §370 q. ED COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM. 375. **The areas of two similar triangles are to each other as the squares of any two homologous** sides. Let the two triangles be ACS and A'CB'. A ACB AJ? Draw the perpendiculars CO and C'O'. A ACB... | |
| Edward Albert Bowser - Geometry - 1890 - 420 pages
...equal ^57^ . D .A. r> O A ABC BC BC BC' ' ' ' A A'B'C' ~ B'C' X B'C' - g^c'' • Q•KD• 378. Cor. **The areas of two similar triangles are to each other as the squares of any two homologous** lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...in the above equality for -=^-, its equal T^^-, A ABC BC BC _ BC' A A'B'C' " B'C' 378. Cor. The arms **of two similar triangles are to each other as the squares of any two homologous** lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides... | |
| Edward Albert Bowser - Geometry - 1891 - 424 pages
...A ABC BC BC EC ' 1 ' A A'B'C 7 " B'C' B'C' ~~ B/C"' ' ' '• 7 " '' X _ 378. Cor. The areas of (wo **similar triangles are to each other as the squares of any two homologous** lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides... | |
| George Albert Wentworth - Geometry - 1894 - 456 pages
...PLANE GEOMETRY. — BOOK IV. COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM. 375. The areas of tivo **similar triangles are to each other as the squares of any two homologous** sides. A 0 B A! O' B' Let the two triangles be ACB and A'GB'. A ACB Al? To prove A A'C'B' Draw the... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...formed by a straight line parallel to the base, and distant 5 feet from the vertex ? 2. Prove that **the areas of two similar triangles are to each other as the squares** of the radii of their inscribed circles. 3. Prove that the area of a circumscribed polygon is equal... | |
| |