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 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
| Henry William Watson - Geometry - 1871 - 320 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 and DEF be... | |
| 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...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 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 Frothingham Bradbury - Geometry - 1872 - 268 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 angle A =... | |
| 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 angle A =: D and... | |
| Euclid - Geometry - 1872 - 284 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... | |
| William Chauvenet - Geometry - 1872 - 382 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 - 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... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...with 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 the angle A... | |
| David Munn - 1873 - 160 pages
...perpendiculars 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... | |
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