 | Marianne Nops - 1882 - 278 pages
...proposition. SUMMARY OP PROPOSITION VIII., THEOREM 5. If in two triangles the, three sides of one are equal to the three sides of the other each to each, the triangles are equal in all respects. Cons.— Nil. AAA Proof. — By superposition. If the triangles... | |
 | Education - 1890 - 384 pages
...physical ligure (as surface or solid) and a mathematical figure (as area or volume). 3. Prove that if two triangles have the three sides of the one equal...to the three sides of the other, each to each, the triangles are equal. 4. Jf the area of a triangle, whose shortest side is six feet, is 4 .4 square... | |
 | Mathematical association - 1883 - 86 pages
...the greater base being greater than the angle of the other. [By Rule of Conversion.] THEOR. 18. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles those are equal which are opposite to equal... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...triangles coincide, and are consequently equal. QED PROPOSITION VII. 305. Theorem.— Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEMONSTRATION. Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BO = EF.... | |
 | Euclides, James Hamblin Smith - 1883 - 376 pages
...sides which subttnd them are also equal. (Kucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles ham the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC,... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...than AC and AD is drawn to D the middle point of BC, shew that the angle ADB is acute. THEOR. 18. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles those are equal which are opposite to equal... | |
 | Mathematical association - 1884 - 146 pages
...than AC and AD is drawn to D the middle point of BC, shew that the angle ADB is acute. THEOK. 18. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angrles those are equal which are opposite to... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...and BC greater than EF, then is the angle BAC greater than the angle EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal...to the three sides of the other, each to each, the triangles are equal in all respects. In the triangles ABC and DEF, let AB be equal to DE, AC to DF,... | |
 | New York (N.Y.). Board of Education - Education - 1885 - 990 pages
...and two adjacent angles in the other, each to each, the two triangles are equal in all respects. If two triangles have the three sides of the one equal...to the three sides of the other, each to each, the two triangles are equal, and the equal angles are opposite the equal sides. If two sides of a triangle... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...former is called a direct, and the latter an indirect demonstration. THEOREM VIII. If two tnangles have the three sides of the one equal to the three...sides of the other, each to each, the three angles wiU also be equal, each to each. Let the two triangles ABC, ABD, have the side AB equal to the side... | |
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If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
