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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
An Elementary Treatise on Plane and Solid Geometry - Page 146
by Benjamin Peirce - 1871 - 150 pages
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Euclid and His Modern Rivals

Lewis Carroll - Geometry - 1885 - 318 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...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...
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Calendar of Dalhousie College and University

Dalhousie University - 1888
...parallel to the 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...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...conversely. 5. 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...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 386 pages
...are proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. V 326. If two triangles have an angle of the one equal to an angle of the othcr, and the including sides proportional, they are similar. In the triangles ABC and A'B'C ' , let...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...of the polygon. D AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 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. Let the triangles ABC and...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...other, have their 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...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...10, find the lengths of the segments BD and CD. 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 A s ABC, A'B'C', let , AB __ AC ZA-ZA, and...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...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...
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The Common Sense of the Exact Sciences

William Kingdon Clifford - Mathematics - 1891 - 312 pages
...famous 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...
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