 | James Maurice Wilson - Geometry - 1868 - 150 pages
...are therefore equal. And if the chord AB is given equal to the chord PQ, then the triangles AOB, POQ have the three sides of the one equal to the three sides of the other; and therefore the angle AOB=\he angle POQ; and therefore also the arc AB = the arc PQ. COR. 1. If the... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...than ABC. PROPOSITION XVII. — THEOREM. ELEMENTS OP GEOMETRY. Let ABC, DBF be two triangles, having the three sides of the one equal to the three sides of the other, eaeh to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0... | |
 | Bernhard Marks - Geometry - 1869 - 180 pages
...angle c, opposite the side A B. I) B PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...AB. (Ax. 5). Hence the theorem; the difference between any two sidei of a triangle, etc. THEOREM XXI. 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 equTl, and the equal angles are opposite the equal sides. In two triangles, as... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie three sides of the one equal to the three sides of the other, each to each, the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB... | |
 | Bernard Marks - Geometry - 1871 - 172 pages
...the side A B. THEOREMS ILLUSTRATED. PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
 | Euclides - 1871 - 136 pages
...If two angles of a triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. -25 q _ Let the three sides of the A s ABO, DEF be equal,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie '.hree sides of the other, each to each, the three angles will also be eqi. il, each to each,... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...likewise those terminating in the other extremity of the base equal to one another. PROPOSITION VIII. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles will also be equal to each other in every other respect, that is, the angles of... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...receive special attention. EQUALITY OP TBIANGLES. PROPOSITION IX. 292. Theorem. — Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEM. — Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC =' EF ; then... | |
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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. 
