 If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...  Elements of Geometry - Page 30by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pagesFull view - About this book
 | Harvard University - Geometry - 1899 - 39 pages
...card-board. PLANE GEOMETRY BOOKS I TO V. BOOK I. ANGLES, TRIANGLES, AND PERPENDICULARS. THEOREM I. If two triangles have two sides and the included angle of one respectively equal to two sides and the included angle of the other, the triangles are equal. THEOREM... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...§ 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to ttvo sides and the included angle of the other, II. They are symmetrical if the equal parts occur in... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...was to be proved. QEF Quod erat faciendum, wh ich was to be done. BOOK I PROPOSITION I. THEOREM 30. If two triangles have two sides and the included angle...included angle of the other, the triangles are equal in all respects. Let the A ABC and DEF have AB = DE, BC = EF, and ZB = ZE To Prove the A ABC and DEF... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...7. THEOREMS ON THE EQUALITY OF TRIANGLES. Two triangles are identically equal if they have — (1) Two sides and the included angle of one equal, respectively, to two sides and the included angle of the other. § 41. (2) A side and the two adjacent angles of one equal, respectively, to a side and... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...questions of this kind. PROPOSITION IV 41. If two triangles have two sides and the included angle of the one equal, respectively, to two sides and the included angle of the other, the triangles are identically equal. EF f E Let ABC and DEF be the two given triangles in which the side AB equals the... | |
 | Theophilus Nelson - Geometry, Modern - 1902 - 154 pages
...triangles equal? What general principle may be inferred from this in regard to two triangles which have two sides and the included angle of one equal,...respectively, to two sides and the included angle of the other? Statement : — 101. Draw a triangle ABC with the sides AB, BC, and CA equal, respectively,... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...was to be proved. QEF Quod erat faciendum , which was to be done. BOOK I PROPOSITION I. THEOREM 30. If two triangles have two sides and the included angle...included angle of the other, the triangles are equal in all respects. Let the A ABC and DEF have AB = DE, BC = EF, and ZB = Z E. To Prove the A ABC and... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...BX? Auth. Conclusion. 28. Problem III. To construct an angle equal to a given angle. THEOREM VI 29. If two triangles have two sides and the included angle...equal respectively to two sides and the included angle of the otJier, the triangles are equal. Hyp. In the A ABC and DEF, let AC=DF, AB = DE, To prove that... | |
 | Joseph Battell - Force and energy - 1903 - 722 pages
...greater side is opposite the greater angle.' "Demonstrated under Figure i (Eighth). PROPOSITION XXII. 1 If two triangles have two sides and the included angle...equal respectively to two sides and the included angle oí the other, the triangles are equal.' "Because the third sides, extending over equal space, are... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...equally distant from AB and BC. Proof. Draw PF _L to AB. Lay off BE = BF and draw PE. A PBF and PBE have two sides and the included angle of one equal respectively to two sides and the included angle of the other, whence ZF = ZE and PF = PE. PE is therefore perpendicular to BC, and P is equally distant... | |
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