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 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
| William Chauvenet - Geometry - 1872 - 368 pages
...of the ratio of similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. 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. Two triangles which have... | |
| Thomas Steadman Aldis - 1872
...of "proportional compasses." 2. Two triangles have their altitudes proportional to their bases, and **an angle of the one equal to an angle of the other,** adjacent to the bases; prove that they are similar. 3. Prove that two quadrilateral figures are similar... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which **have an angle of the one equal to an angle of the other, and the sides** containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A... | |
| David Munn - 1873
...opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. 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 47 IX. The areas of similar... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which **have an angle of the one equal to an angle of the other, and the sides** containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A... | |
| Euclides - 1874 - 342 pages
...of the intercepted area, according as they intersect internally or externally. 15. If two trapeziums **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Euclides - 1874 - 234 pages
...the two triangles are equal, ABxAC=POxOQ, therefore ^? - 29 \)L .AO that is, equal triangles which **have an angle of the one equal to an angle of the other,** have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular... | |
| L J V. Gerard - 1874
...angles are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which **have an angle of the one equal to an angle of the other,** have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having **an angle of the one equal to an angle of the other, and** tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB : DE... | |
| Richard Wormell - 1876
...same demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and **have an angle of the one equal to an angle of the other,** then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
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