 | Georgia. Department of Education - Education - 1917 - 584 pages
...chord; and, Conversely, the greater of two chords subtends the greater (minor) arc. 4. Demonstrate: The areas of two similar triangles are to each other as the squares of any two homologous sides. 5. Demonstrate: The area of a circle is equal to one-half the product of its circumference by... | |
 | Morris Kline - Mathematics - 1964 - 513 pages
...subject matter was really the summation and culmination of the mathematics of the classical period. That the areas of two similar triangles are to each other as the squares of corresponding sides was of great interest to Euclid, but that the area of any one single triangle... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 pages
...proportional between the two sides inclosing the angle.) SIMILAR TRIANGLES PROPOSITION XI. THEOREM 399. The areas of two similar triangles are to each other as the squares of any two homologous sides. ADB A' Given the two similar triangles ABC and A'B'C*. AABC AB2 To prove that AA'B'C' A'B' Proof.... | |
 | 1919 - 496 pages
...remote is the greater. 2. Prove that a parallelogram inscribed in a circle is a rectangle. 3. Prove that the areas of two similar triangles are to each other as the squares of any two homologous sides. Will this theorem hold for two similar polygons of n sides? Prove your answer. 4. If two chords... | |
 | William Weller Strader, Lawrence D. Rhoads - Geometry, Plane - 1927 - 434 pages
...Mutually equiangular parallelograms have the same ratio as the products of two adjacent sides. 11. The areas of two similar triangles are to each other as the squares of two corresponding medians. 12. The areas of two similar triangles have the same ratio as the squares... | |
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The areas of two similar triangles are to each other as the squares of any two homologous sides. 
