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" ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if... "
The Essentials of Geometry (plane) - Page 47
by Webster Wells - 1898 - 242 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
...coincide, and are equal in 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
...to a side and the 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
...perimeter, 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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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...(§413.) Whence, BB'C'C is a parallelogram, and BC = B'C'. Therefore, A ABC = A A' B'C'. [Two triangles are equal when the three sides of one are equal respectively to the three sides of the other.] (§69.) Whence, Z BAC = Z B'A'C'. [In equal figures, the homologous parts are equal.] (§ 66.) II. To prove...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...proportional to the 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
...coincide throughout, and are equal. PROPOSITION XVII. THEOREM. 69. Two triangles are equal when tlie three 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. E Place the...
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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
...vertices 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 - 1896 - 214 pages
...vertices 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 AlF^PA x PB. 4. The radius...
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