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 and Solid Geometry - Page 146by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
| Henry William Watson - Geometry - 1871 - 320 pages
...AGH, therefore the triangle ABC is similar to the triangle DEF. PROPOSITION 18. If two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportionals, the triangles shall be similar. Fig. 25. Let ABC and DEF... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, be the two triangles having the... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...triangles is the 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... | |
| Thomas Steadman Aldis - 1872 - 84 pages
...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... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...bisecting line meets AC produced, the segments of the base (59) are AE and CE. (I. 17.) (1. 45.) (16.) 61 i Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC:ADE—ABXAC:AD... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...line meets AC produced, the segments of the base (59) are AE and CJEL (I. 17.) (1. 45.) (16.) 61 1 Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC:... | |
| Euclid - Geometry - 1872 - 284 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... | |
| 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... | |
| David Munn - 1873 - 160 pages
...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... | |
| |