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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 47
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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Riders in Geometry

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...
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The Thirteen Books of Euclib's Elements.

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...
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Paractical Geometry Based on the Various Geometry Books by Godfrey and Siddons

...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...
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Solutions of the Exercises in Tyler's Euclid

...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...
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Annual Report of the Public Schools of the Province of British Columbia

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....

The Elements of Plane Geometry

Euclid - 1845 - 262 σελίδες
...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...
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A Shorter Geometry

...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...
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Elementary Geometry

Olaus Henrici - 1888 - 188 σελίδες
...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...
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Geometry for Beginners

...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...
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Challenge and Thrill of Pre-College Mathematics

V Krishnamurthy, C R Pranesachar - 2007 - 704 σελίδες
...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...
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