 | William Chauvenet - Mathematics - 1872 - 382 pages
...theorems, and the sum of these areas will be the area of the polygon. PROPOSITION VII.— THEOREM. 20. Similar triangles are to each other as the squares of their homologous sides. Let ABC, A'B'C' be similar tri- <« angles ; then, ABC BC* DC A'B'C' B'C" Let AD, A'D', be the altitudes.... | |
 | Education - 1873 - 444 pages
...triangle meet in the same point. 5. Problem.—To describe a circle through three given points. 6. Similar triangles are to each other as the squares of their homologous sides. 7. Define: (a) equal figures; (b) equivalent figures; (c) timilar figures. 8. What is the sum of the... | |
 | 1873 - 192 pages
...the circle. 6. Prove that two regular polygons of the same number of sides are similar. 7. Prove that similar triangles are to each other as the squares of their homologous sides. 8. Show how the area of a polygon circumscribed about a circle may be found; then how the area of a... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...the squares BIKC and AGHB; or 28. Corollary. AC* = AI? + Btf Since Tc* = Ti? + Fc" THEOREM XIII. 29i Similar triangles are to each other as the squares of their homologous sides. Let ABC and DEF be two B similar triangles; then ABC : DEF = AC 2 : iTF* Draw BG and EH perpendicular... | |
 | David Munn - 1873 - 160 pages
...angle of the other, are to each other as the products of the sides including the equal angles 47 IX. The areas of similar triangles are to each other as the squares of their like sides 48 X. The areas of similar polygons are to each other as the squares of their like... | |
 | Wisconsin. Department of Public Instruction - Education - 1873 - 456 pages
...triangle meet in the same point. 5. Problem. — To describe a circle through three given points. 6. Similar triangles are to each other as the squares of their homologous aides. 7. Define : (a) equal figures ; (b) equivalent figures ; (c) similar figures. 8. What is the... | |
 | Wisconsin - Wisconsin - 1874 - 1050 pages
...triangle meet in the same point. 5. Problem. — To describe a circle through three given points. 6. Similar triangles are to each other as the squares of their homologous sides. 7. Define: (a) equal figures ; (b) equivalent figures; (c) similar figures. 8. What is the sum of the... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...: ABE : ABC ; that is, ABE is a mean proportional between ADE and ABC. , PROPOSITION XXV. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and G to... | |
 | David Munn - Measurement - 1874 - 374 pages
...^^15x15x4x2 2. The area of the triangle whose sides are 15, 18, 21, s x 12 x 9 x 6, or 54 ^6. Then as the areas of similar triangles are to each other as the squares of their corresponding sides, we have x2 54 = 754 V6 3 J6 Again, for the other sides, we have <54 .76... | |
 | Rutgers University. College of Agriculture - 1877 - 310 pages
...3. If two chords intersect each other in a circle, their segments art reciprocally proportional. 4. Similar triangles are to each other as the squares of their homologous side.1?. 5. The area of a regular polygon is equal to one-half the produet of its apothegm by its perimeter.... | |
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Similar triangles are to each other as the squares of their homologous sides. 
