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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...
Elements of Plane Geometry: For the Use of Schools - Page 71
by Nicholas Tillinghast - 1844 - 96 pages

## Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...triangles and trapezoids are then computed by the previous theorems. 198 PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and...

## Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...right triangles and trapezoids are then computed by the previous theorems. PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and...

## Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...is a mean proportional between the segments of the other. 51. Two parallelograms are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. 52. Two rectangles are similar if two adjoining pairs of homologous sides...

## Annual Report of the Commissioners ..., Volume 72

1906 - 818 pages
...square of the line which touches it. 2. To describe a circle about a given regular pentagon. 3. Equal triangles which have an angle of the one equal to an angle of the other have their sides about those angles reciprocally proportional ; and triangles which have an angle of...

## The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1907 - 534 pages
...and E respectively, so that OA : AD = CB : BE, prove that DE is parallel to AB. 8. 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, prove the triangles equal in area. 9. Given any two rectilinear figures,...

## Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...is a mean proportional between the segments of the other. 51. Two parallelograms are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. 52. Two rectangles are similar if two adjoining pairs of homologous sides...

## Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908 - 328 pages
...half its area, from whose sides the given circle shall cut off equal chords. (25) 43. If two triangles have an angle of the one equal to an angle of the other and the sides about those angles proportional, show that the triangles are equiangular to one another. Find a point P in...

## School Algebra, Volume 1

William Ernst Paterson - Algebra - 1908 - 614 pages
...are equiangular, the ratios of corresponding aides are equal. Theorem III. If two triangles have one angle of the one equal to an angle of the other and the aides about the equal angles proportional, then' the triangles are equiangular. 237. Theorem I leads...