 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'...  A Supplement to the Elements of Euclid - Σελίδα 560των Daniel Cresswell - 1825 - 582 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | William Chauvenet - 1871 - 380 σελίδες
...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, be the two triangles having the... | |
 | William Chauvenet - 1871 - 380 σελίδες
...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 - 1872 - 382 σελίδες
...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 - 1872 - 124 σελίδες
...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... | |
 | William Frothingham Bradbury - 1872 - 262 σελίδες
...(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... | |
 | Euclid - 1872 - 284 σελίδες
...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 - 84 σελίδες
...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 Chauvenet - 1872 - 382 σελίδες
...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... | |
 | Benjamin Greenleaf - 1873 - 202 σελίδες
...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... | |
 | David Munn - 1873 - 160 σελίδες
...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... | |
| |
