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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...
Plane Geometry - Page 72
by John Charles Stone, James Franklin Millis - 1916 - 278 pages
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## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...THEOREM. 106. Two triangles are equal in all respects when two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. D Ai In the triangles ABC and A' B' C', let AB = A' B', AC = A' C', ZA = Z A'. We are to prove AABC =...
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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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## The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...672. Two triangles on the same sphere or on two equal spheres are either equal or symmetrical when two sides and the included angle of one are equal respectively to two sides and the included angle of the other. I. In the triangles ABC and DEF, let the sides AB and AC and the included angle A be...
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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 - 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 - 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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