 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...included side of the one are respectively equal to the corresponding parts of the other. 3rd. When the three sides of the one are respectively equal to the three sides of the other. 12. Prove that when two sides of a triangle are respectively equal to two sides of another, but the... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...included side of the one are respectively equal to the corresponding parts of the other. 3rd. When the three sides of the one are respectively equal to the three sides of the other. Theorems and Problems. 1. The line that joins the vertex to the middle point of the base of a triangle... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...follow A = D, AB = DE, and AC = DF. PROPOSITION XXII.— THEOREM. 80. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. In the triangles ABC, DEF, let AB be equal to DE, AC to DF, and BC to EF; then, the triangles are equal.... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...side of the one are respectively equal to two angles and the included side of the other ; or 3rd. When the three sides of the one are respectively equal to the three sides of the other. From the Corollary to Prop. 23 it follows that case 2 may be extended to the case of two angles, and... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...in AD or AD pro. duced, as E'H'. Now, the cr G two triangles AE'B and DH'C FIG. 223.• are equal, because the three sides of the one are respectively...triangle AE'B = ABCH' - DH'C. But ABCH' - AE'B = E'BCH' = EFCH ; and ABCH' - DH'C = ABCD. Hence, ABCD = EFCH. QED 313. COR. — Any parallelogram is equivalent... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...enough, to determine the triangle. THREE SIDES EQUAL. 282. Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Let the side BD be equal to AI, the side BC equal to AE, and CD to EI ; then the two triangles are... | |
 | James Maurice Wilson - 1872 - 160 pages
...P' would fall on P, and Qf on QP. Therefore Qf = QP; And therefore in the triangles QOP, QOP', since the three sides of the one are respectively equal to the three sides of the other, the angle QOP = the angle QOP'; And therefore QOP is a right angle; that is, PO is at right angles... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...will follow A = D, AB = DE, &ndAC = DF. PROPOSITION XXII.— THEOREM. 80. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. In the triangles ABC, DEF, let AB be equal to DE, AC to DF, and BC to EF; then, the triangles are equal.... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...follow A = D, AB = DE, &ndAC=DF. PROPOSITION XXII—THEOREM. 80. Two triangles are equal when tlie three sides of the one are respectively equal to the three sides of the other. In the triangles ABC, DEF, let AB be equal to DE, AC to DF, and BC to EF; then, the triangles are equal.... | |
 | James Maurice Wilson - 1878 - 450 pages
...to prove that OC is perpendicular to AB. Proof. Join OA, OB. Then because in the triangles OAC, OBC, the three sides of the one are respectively equal to the three sides of the other; therefore the angles O CA, OCB opposite to the equal sides OA, OB are equal (i. 15), and are therefore... | |
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Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. 
