 If two triangles have three sides of the one equal respectively to three sides of the other, the triangles are equal in all -respects. Let ABC and DEF be two A, having AB = DE, BC = EF, and AC = DF. To Prove A ABC and DEF equal in all respects. Proof....  Elements of Plane and Solid Geometry - Page 31by Alan Sanders - 1908 - 384 pagesFull view - About this book
 | Euclides - 1852 - 48 pages
...remaining angles of the one, are respectively equal to the remaining angles of the other, and the two triangles are equal in all respects. Let ABC and DEF be two triangles, having the side AB equal to DE, the side AC equal to DF, and the angle A equal to the angle... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...the other (§ 88 c). 15. When two triangles have the three sides of the one respectively equal to the three sides of the other, the triangles are equal in all respects (§ 88</). Properties of parallels. 16. Two straight lines perpendicular to a third are parallel (§... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...each other). .-. CDD'C'isa.n. § 13G • • O -Lf OU •, v 1 o4 .'. AADC = A A' D' C', §108 (having three sides of the one equal respectively to three sides of the otlier). (being homologous A of equal QED •463. COROLLARY. If two angles lie in different planes... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...OE=OB, §138 (the diagonals of au bisect each other) ; AO = AO, Iden. .-.A AOE = AA OB, §108 (having three sides of the one equal respectively to three sides of the other) ; .-. ¿ AOE = ¿ A OB, (being homologous A of equal A) ; .-.Z A0 E ami ZA О5 are rt. A §25 ( When... | |
 | Euclides - 1883 - 176 pages
...point in either is equidistant from the extremities of the other (Prop. 4). 14. If two quadrilaterals have three sides of the one equal respectively to three sides of the other, and likewise the angles contained by the equal sides equal in each, the figures shall be equal in every... | |
 | Mathematical association - 1884 - 146 pages
...the arms of the angle BAC, shew that OA bisects the angle BAC. EXERCISES. 29. If two quadrilaterals have three sides of the one equal respectively to three sides of the other taken in order, and have likewise the angles contained by those sides equal to one another, each to... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...the arms of the angle BAC, shew that OA bisects the angle BAC. EXERCISES. 29. If two quadrilaterals have three sides of the one equal respectively to three sides of the other taken in order, and have likewise the angles contained by those sides equal to one another, each to... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...than, the third side of the second. 691. COROLLARY. Therefore, by 688, two spherical triangles having three sides of the one equal respectively to three sides of the other are either congruent or symmetrical. PROBLEM I. 692. To bisect a given spherical angle. Let BAC^ the... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...than, the third side of the second. 691. COROLLARY. Therefore, by 688, two spherical triangles having three sides of the one equal respectively to three sides of the other are either congruent or symmetrical. PROBLEM I. 692. To bisect a given spherical angle. Let BAC be... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...Hence in the A AEffa.nd A' B'C', EH= B'C', AE= A'B', and AH= A'C'. :. AA EH= A A' B'C', § 160 (having three sides of the one equal respectively to three sides of the other). But A AEH is similar to A ABC. :. A A' B'C' is similar to A ABC. a ED 325. SCHOLIUM. The primary idea... | |
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