 | Edward Albert Bowser - 1890 - 414 sivua
...Theorem. 375. The areas of two triangles having 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. Hyp. Let ABC, ADE be the two As having the common /_ A. AABC AB X AC Toprove ___ = ____. Proof. Join... | |
 | Webster Wells - 1890 - 560 sivua
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a... | |
 | William Chauvenet - 1893 - 340 sivua
...EXERCISE. Theorem. — Two triangles having 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. Suggestion. Let ADE and ABC be the two triangles. Draw BE, and compare the two triangles with AEB.... | |
 | 1893 - 408 sivua
...Prove that 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. 16 6 Prove that the area of a regular polygon is equal to half the product of its perimeter and apothem.... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 522 sivua
...the base, PROPOSITION XV. Two triangles which are mutually equiangular are similar. PROPOSITION XVI. If two triangles have an angle of one equal to an angle of the other, and the side* including the equal angles proportional, the triangles are similar. PROPOSITION XVII.... | |
 | George Albert Wentworth, George Anthony Hill - 1894 - 150 sivua
...side and equal to onehalf of it. 4. The two tangents to a circle from an outside point are equal. 5. If two triangles have an angle of one equal to an angle of the other they are to each other as the product of the sides including the equal angles. 6. From the obtuse angle... | |
 | 1922 - 560 sivua
...and there is no limit to the number of independent solutions. We can also state now this theorem: // two triangles have an angle of one equal to an angle of the other, and if in each triangle the n-th power of the side opposite is equal to the sum of the n-th powers... | |
 | Joe Garner Estill - 1896 - 186 sivua
...Assuming that 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, prove that the bisector of an angle of a triangle divides the opposite side into parts which are proportional... | |
 | George Albert Wentworth - 1896 - 68 sivua
...altitude. 374. 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. 375. The areas of two similar triangles are to each other as the squares of any two homologous sides.... | |
 | George D. Pettee - 1896 - 272 sivua
...PROPOSITION VIII 255. Theorem. Two triangles having an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. Appl. Cons. Dem. Prove ABC = AB x AC ADE AD x AE Draw DC ABC = AB ADC AD ADC = AC ADE AE altitudes... | |
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If two triangles have an angle of one equal to an angle of the other, and... 
