| William Chauvenet - Geometry - 1871 - 380 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 an angle... | |
| Henry William Watson - Geometry - 1871 - 285 pages
...triangle 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...an angle of the other 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, b« the two triangles having the... | |
| 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 an angle... | |
| Euclid - Geometry - 1872 - 261 pages
...be 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
...diagonals proportionals, each to each, prove that they are similar. THEOREM XIII. If two triangles **have an angle of the one equal to an angle of the other,** and the sides about the equal angles proportional, they shall be similar. Let ABC and PQR be two triangles,... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...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... | |
| William Frothingham Bradbury - Geometry - 1872 - 238 pages
...(I. 35^, and similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having **an angle of the one equal to an angle of the other,** and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e... | |
| David Munn - 1873
...on it from the 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 triangles... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...the triangle ABC; 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... | |
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