 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...They are almost sufficient of themselves for all applications to subsequent reasoning, and for the solution of all problems ; since the general properties...proportional, are similar. Let the two triangles ABC, PEF have the angle A equal to the angle D, and the sides containing these angles proportional, so that... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...They are almost sufficient of themselves for all applications to subsequent reasoning, and for the solution of all problems ; since the general properties...the two triangles ABC, DEF have the angle A equal to the angle D, and the sides containing these angles proportional, so that AB:DE::AC:DF; then the triangles... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...arcs. 5. Prove that parallelograms which have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the one equal to an angle of the other are to each other as the rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast... | |
 | 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 two triangles... | |
 | William Chauvenet - Geometry - 1871 - 380 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, be the two triangles having the... | |
 | 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 - 262 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... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing. 
