 | William Chauvenet - Geometry - 1887 - 336 pages
...similarity of ABC and A'B'C', BC = AB . B'C' A'B" hence AD BC A'D' X B'C' and we have ABC A'B'C' 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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...similarity of ABC and A'B'C', BC AB hence A'D and we have _. B'c' 373-- 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... | |
 | Dalhousie University - 1888 - 212 pages
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must be... | |
 | Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles have an angle of the one equal to an angle of the other, their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...A'B'C' is similar to the A ABC. QED EXERCISE. Proposition 1 8. Theorem. 314. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Hyp. In the AS ABC, A'B'C', let AB AC nv To prove A ABC... | |
 | Euclid - Geometry - 1890 - 442 pages
...sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, the triangles have the same area. Let A" ABC, AD... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...given by Euclid, about 300 BC (Prop. 47, Book I. Euclid). Proposition 8. 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... | |
 | William Kingdon Clifford - Mathematics - 1891 - 312 pages
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respsctively equal, they must be equal in all particulars. For if we take up... | |
 | Joe Garner Estill - 1896 - 214 pages
...whatever direction the chord is drawn. 6. Prove the ratio between the areas of two triangles which have an angle of the one equal to an angle of the other. Define area. 7. Define a regular polygon and prove that two regular polygons of the same number of... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...trapezoid is equal to the product of the median by the 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... | |
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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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... 
