| Thomas Hadyn Ward Hill
...P, Q, R respectively. Show that the triangle PQR is also equilateral. 15. ABC, DBC are two triangles **on the same base BC and on the same side of it,** and A = D, ABC = DCB. Prove that the straight line joining the point of intersection of AC and BD to... | |
| Euclid
...base and on the same side are also in the same parallels. Let ABC, DBC be equal triangles which are **on the same base BC and on the same side of it** ; S [I say that they are also in the same parallels.] And [For] let AD be joined ; I say that AD is... | |
| ...Also prove that, if AC, BD intersect at O, A OCD is isosceles. Ex. 34. Two triangles ABC, DCB stand **on the same base BC and on the same side of it;** prove that AD is parallel to BC if AB — . DC and AC = DB. Ex. 36. The triangles ABC and A'BC are... | |
| ...LABD= LACD; .: L OQS= L ORP. .: a Q will go round PQRS. 278, 65. Any number of triangles are described **on the same base BC, and on the same side of it** having their vertical angles equal, and perpendiculars, intersecting at D, are drawn from Ji and C... | |
| British Columbia. Superintendent of Education - 1897
...other sides of the triangle, but will contain a greater angle. 4. (a.) Equal triangles on the same base **and on the same side of it are between the same parallels.** (b.) All the exterior angles of any rectilineal figure are together equal to four right angles. 5.... | |
| Euclid - 1845 - 262 pages
...is a quadrilateral in which AB = At> and BC<:CD ; show that 3. ABC and DBC are isosceles triangles **on the same base BC and on the same side of it** ; prove that L. ABD= L. ACD. 4. The base BC of an isosceles triangle ABC is produced to D ; show that... | |
| ...prove that PQR is equilateraL tEx. 389 ABC is an equilateral triangle ; DBC is an isosceles triangle **on the same base BC and on the same side of it,** and / BDC--^ / BAC. Prove that AD = BC. tEx. 8BO. How many sides has the polygon, the sum of whose... | |
| Olaus Henrici - Congruences (Geometry) - 1888 - 188 pages
...line joining their vertices bisects the base at right angles. tEx. 841. Two triangles ABC, DCB stand **on the same base BC and on the same side of it;** prove that AD is parallel to BC if AB = DC and AC = DB. tEx. 842. In the diagonal AC of a parallelogram... | |
| ...prove that PQR is equilateral. tEx. 389. ABC is an equilateral triangle; DBC is an isosceles triangle **on the same base BC and on the same side of it,** and L BDC = ^/ BAC. Prove that AD = BC. tEx. 39O. How many sides has the polygon, the sum of whose... | |
| V Krishnamurthy, C R Pranesachar - Mathematics - 2007 - 704 pages
...ABCD, AC bisects angles A and C, show that AC is perpendicular to BD. 10. ABC and DBC are two triangles **on the same base BC and on the same side of it** such that BA = CD and BD = CA. If AC and BD meet at O, prove that AOBA is congruent to A0CD. 1 1. Deduce... | |
| |