 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 - Σελίδα 146των George Albert Wentworth - 1881 - 250 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Henry William Watson - 1871 - 320 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1872 - 382 σελίδες
...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... | |
 | William Frothingham Bradbury - 1872 - 262 σελίδες
...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 - 1872 - 124 σελίδες
...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:... | |
 | 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... | |
 | Euclid - 1872 - 284 σελίδες
...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 - 1873 - 202 σελίδες
...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 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... | |
 | Benjamin Greenleaf - 1874 - 206 σελίδες
...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... | |
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