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" There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the... "
General Mathematics - Page 115
by Raleigh Schorling, William David Reeve - 1922
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 348 pages
...and the inFif' '°°' cluded angle completely determine a Theorem. — Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Exercises. — 1. Construct a parallelogram, the two sides being 44™ and 66°°, and...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 200 pages
...If two parts are given ? If the three angles are given ? 14. Theorem. — Two triangles are equal, if two sides and the included angle of one are equal,...respectively, to two sides and the included angle of the other, HYPOTHESIS. A ABC and DEF, AB=DE, AC CONCLUSION. A ABC = A DEF. PROOF. We may divide...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 202 pages
...? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, if two sides and the included angle of one are equal,...respectively, to two sides and the included angle of the other. HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. -^ BDE A ABC = A DEF. FI°- 67PROOF....
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1889 - 200 pages
...given? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, if two sides \ and the included angle of one are equal, respectively, vto two sides and the included angle of the other, HYPOTHESIS. j} A ABC and DEF, AB=DE, AC=DF, CONCLUSION....
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Pacific Educational Journal, Volume 9

Education - 1893 - 568 pages
...triangle by measuring two sides and included angle of a given triangle. Theorem: Two triangles are equal if two sides and the included angle of one are equal,...respectively, to two sides and the included angle of the other. 13. Theorem: i. In an isosceles triangle, the angles opposite the equal sides are equal....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...which is not in the right bisector of a straight line is unequally distant from the ends of the line. and the included angle of one are equal respectively to two sides and the included angle of the other. 146. Theorem. Two triangles are equal if two angles and a side of one are equal respectively...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...prove AB > BC — A C. We have AB + AC > BC. PROPOSITION XV. THEOREM. 63. Two triangles are equal when two sides and the included angle of one are equal respectively to tivo sides and the included angle of the other. a ABDE In the triangles ABC and DEF, let AB = DE, AC...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...greater face angle. PROPOSITION XXVI. THEOREM &73. Two triangles on the same sphere are equal : I. If two sides and the included angle of one are equal respectively to two sides and the included angle of the other. II. If a side and the two adjacent angles of one are equal respectively to a side and...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...the greater face angle. PROPOSITION XXVI. THEOREM 873. Two triangles on the same sphere are equal: I. If two sides and the included angle of one are equal respectively to two sides and the included angle of the other. II. If a side and the two adjacent angles of one are equal respectively to a side and...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...the shortest line between two points.] (Ax. 4) PROP. XV. THEOREM. 63. Two triangles are equal when two sides and the included angle of one are equal respectively to two sides and the included angle of the other. C BDE Given, in &ABC and DEF, AB = DE, AC=DF, and Z A = Z D. To Prove A ABC = A DEF....
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