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 Geometry - Page 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...ABG, DEH are equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles **having an angle of the one equal to an angle of the other, and the sides** including these angles proportional, are similar. In the triangles ABC,DEF let tiifl angle A =: D and... | |
| William Chauvenet - Geometry - 1872 - 368 pages
...square 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... | |
| Euclid - Geometry - 1872 - 261 pages
...right, the remaining angles will be right angles. FIRST BOOK. COR. 2. — If two parallelograms have **an angle of the one equal to an angle of the other,** the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
| 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
...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
...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
...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... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...respects; (i.5) .'. A FGH is equiangular to &ABC, Also, If two A s have one angle of the one equal to one **angle of the other, and the sides about the equal angles proportional,** then shall the A s be equiangular. B CG ff Let ABC, FGH be two A s, having iBAC=i GFH, and such that... | |
| Euclides - 1874
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have **an angle of the one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be... | |
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