 The areas of two similar triangles are to each other as the squares of any two homologous sides.  Plane Geometry - Page 207by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...square feet and 17 square feet. What distinction is to be made between the two cases ? 4. Prove that the areas of two similar triangles are to each other as the squares of any two corresponding altitudes. 5. One side of a polygon measures 8 feet and its area is 120 square feet.... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...canceling A ABE, we have the proportion Ax. 3 AABC ABxAC = — • OED PROPOSITION VIII. THEOREM 333. The areas of two similar triangles are to each other as the squares on any two corresponding sides. A ~ ~ B A' £' Given the similar triangles ABC and A'B'C'. „, .,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...the other are to each other as the products of the sides including the equal angles. 194. Theorem V. Similar triangles are to each other as the squares of any two corresponding sides. 195. Corollary 1. The areas of two similar polygons are to each other as the squares... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...contact and terminated by the circles are proportional. Apply Ex. 2 170 SIMILAR TRIANGLES 416. THEOREM. The areas of two similar triangles are to each other as the squares of any two homologous sides. the similar A ABC and A' B'C', with BC and B'C' a pair of homologous sides, area A ABC BC2 Given... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...the greatest mathematician of all time. NEWTON BOOK IV. PLANE GEOMETRY PROPOSITION VIII. THEOREM 375. Two similar triangles are to each other as the squares of any two homologous sides. E *' Given: Similar A ABC and DEF. To Prove: A ABC AB BC' A DEF DEZ Proof : Denote a pair of... | |
 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...requested to state on cover of answer-book what text-book of Geometry he used in preparation. 1. Prove that the areas of two similar triangles are to each other as the squares of their corresponding sides, or as the squares of their corresponding altitudes. 2. Prove that if... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...2. CD A ABC _ ^AB-CD = AB A A'B'C' ~ i • A'B' • C'D' ~ A'B' • C'D' A ABC § 333 ; Ax. 6, § 51 Note. — Since the ratio of two homologous lines...ratio of A ABC to A A'B'C', if they are similar, and: (a) if AB = 3 A'B' ? (6) if AB = A'B' ? (c) if AB = f A'B' ? 4. ' AA'B'C' \A'B'j ] \C'D') }„,. CD... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...right triangle with the square on one leg. K N B NX / AREAS OF POLYGONS PROPOSITION X. THEOREM 343. The areas of two similar triangles are to each other as the squares of any -two homologous sides. Hypothesis. AB and A'B' are homologous sides of similar A ABC and A'B'C' respectively. Conclusion.... | |
 | William Betz - Geometry - 1916 - 536 pages
...(see figure), and the height of the . crown CD is 6 in. Find the radius of the circular arch. 399. The areas of two similar triangles are to each other as the squares of any two homologous sides. D D' B' Given the two similar triangles ABC and A'B'C. To prove t//<tt ABC A A'B'C1 JTgi2 Proof.... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...The area of a trapezoid is equal to half the product of its altitude by the sum of its bases. 355. The areas of two similar triangles are to each other as the squares of any two homologous sides. 358. The areas of two similar polygons are to each other as the squares of any two homologous... | |
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