| Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 167 pages
...and XLII, 4.] Proposition 40. 142. Triangles of equal area on equal bases in the same straight line **and on the same side of it, are between the same parallels.** Let ABC, DEF represent triangles on equal bases BC, EF in the same straight line BF, and on the same... | |
| Henry Martyn Taylor - 1895 - 657 pages
...must have one pair and may have two pairs of equal angles. 2. ABC, J)BC are two isosceles triangles **on the same base BC, and on the same side of it** : shew that AD bisects the vertical angles of the triangles. 3. If the opposite sides of a quadrilateral... | |
| George D. Pettee - Geometry, Plane - 1896 - 253 pages
...bisector, and a parallel to the other side, form an isosceles triangle. 76. ABC and DBC are two triangles **on the same base BC and on the same side of it,** such that ^41? = DC, AC = DB; and AC intersects DB at O. Prove that BOC is isosceles. 77. If a diagonal... | |
| Seymour Eaton - 1899 - 340 pages
...base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DEC be **on the same base BC, and on the same side of it** : then they shall be between the same parallels. Construction : Join AD. Proof: AD shall be parallel... | |
| Education - 1899
...within the quadrilateral A KCD, prove that BO + CD + DA > PA + РП. 3. Equal triangles on the same base **and on the same side of it are between the same parallels.** If POQ, ROS are two straight lines through 0, and the triangles POJt, QOS are equal in area, prove... | |
| Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 304 pages
...means of I. 5) that the angle ABD = the angle ACD. ' 3. ABC, DBC are two isosceles triangles drawn **on the same base BC and on the same side of it** : employ i. 5 to prove that the angle ABD = the angle ACD. PROPOSITION 7. THEOREM. On the same base,... | |
| University of Toronto - 1901
...greater than the sum of the diagonals, and less than twice that sum. 2. Equal triangles on the same base, **and on the same side of it, are between the same parallels.** (I. 39.) If ЛВС and ABD are two equal triangles on the same side of the line AJi Ħaid tiie parallelogram... | |
| Eldred John Brooksmith - Mathematics - 1901
...that the sum of the lines DF, FG, GE has the least possible value. 2. Equal triangles on the same base **and on the same side of it are between the same parallels.** Use this proposition to show that the straight line joining the middle points of two sides of a triangle... | |
| 1901
...Inspector. Mr. CUSSEN, District Inspector. SECTION A. 1. Prove that equal triangles on the same base **and on the same side of it are between the same parallels.** 2. The angles at the base of an isosceles triangle are equal, and if the equal sides be produced, the... | |
| University of Sydney - 1902
...side, &c. Complete this enunciation, and prove the proposition. 3. Equal triangles on the same base **and on the same side of it are between the same parallels.** 4. Straight lines are drawn to bisect the angles at the base BC of an isosceles triangle ABC and to... | |
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