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" Two triangles are congruent if * (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other... "
Introduction to Geometry: A Manual of Exercises for Beginners - Page 67
by William Schoch - 1904 - 137 pages
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Harvard Examination Papers

1873 - 192 pages
...angle ? Why ? 2. To inscribe a circle in a given triangle. 3. Prove that two triangles are equal if the three sides of one are equal respectively to the three sides of the other. 4. Define Similar Polygons. 6. Prove that every equilateral polygon inscribed in a circle is regular....
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...all respects. QED GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Two triangles are equal when the three sides of ; one are equal respectively to the three sides of the other. B B' In the triangles ABC and A' B' C', let AB = A' B', A С = A' C', BC=B' C'. We are to prove Л...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...homologous acute angle of the other. PROPOSITION XXI. THEOREM. 83. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. In the triangles ABC and DEF, let the side AB be equal to DE, BC to EF, and CA to FD. To prove that...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...but greater than half the perimeter. PROPOSITION XXXIII. THEOREM. 160. Two triangles are equal if the three sides of one are equal respectively to the three sides of the other. B JB' In the triangles ABC and A'B'C', let AB = A'B', AC^A'ff, BC= B'C'. To prove A ABC= A A'B'C'....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...adjacent sides. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, June, 1892. 1. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. 2. In the same circle, or in equal circles, equal chords are equally distant from the centre. 3. If...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...? which side is equal to BC? PROPOSITION XVII. THEOREM. 69. Two triangles are equal when the threc sides of one are equal respectively to the three sides of the other. In the triangles ABC and DEF, let AB = DE, BC = EF, and CA = FD. To prove A ABC = A DEF. Place the...
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 186 pages
...is less than the perimeter, but greater than half the perimeter. 2. Two triangles are equal if the three sides of one are equal respectively to the three sides of the other. 3. Construct through a point, P, exterior to a circle, a secant PAB so that AB" 2 = PA x P B. of the...
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Numerical Problems in Plane Geometry with Metric and Logarithmic Tables

Joe Garner Estill - Geometry - 1896 - 168 pages
...is less than the perimeter, but greater than half the perimeter. 2. Two triangles are equal if the three sides of one are equal respectively to the three sides of the other. 3. Construct through a point, P, exterior to a circle, a secant PABsothat A^J = PA x PB. of the tangents,...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...angles of one are equal respectively to a side and the two adjacent angles of the other. III. If the three sides of one are equal respectively to the three sides of the other. Provided in each case that the parts given equal are arranged in opposite order in the two triangles....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...angles of one are equal respectively to a side and the two adjacent angles of the other. III. If the three sides of one are equal respectively to the three sides of the other. Provided in each case that the parts given equal are arranged in the same order in both triangles....
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