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... Elements of Geometry - Page 379by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pagesFull view - About this book
| 1873 - 192 pages
...an 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.... | |
| George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...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... | |
| 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'.... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...problem, corollary. 2. Under what conditions are two triangles equal ? Prove that two triangles are equal if the three sides of one are equal respectively to the three sides of the other. For those offering two books of Euclid. 3. The opposite sides and angles of a parallelogram are equal... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...equal, and the greater diedral angle is opposite the greater face angle. PROPOSITION XXVI. THEOREM 873. Two triangles on the same sphere are equal: I. If...therefore be placed in coincidence. At the same time the triangle/ coincide. Therefore the two given triangles are equal. QED PROPOSITION XXVII. THEOREM 874.... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...triangles are equal. p.. ED PROPOSITION XV. THEOREM 785, Two triangles on the same sphere are symmetrical: I. If two sides and the included angle of one are...each case that the parts given equal are arranged in opposite order in the two triangles. Proof. — Form the symmetrical triangle of the first triangle.... | |
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