 | Webster Wells - Geometry - 1899 - 450 pages
...parallelogram divides it into two equal triangles. PRoP. XXXVIII. THJSOREM. 109. (Converse of Prop. XXXVII, I.) If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given, in quadrilateral ABCD, AB = CD and BC = AD. To Prove ABCD a O. Proof. Draw diagonal AC. In A... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...are everywhere equally distant. DC For if AB and DC are parallel, PROPOSITION XXXIV. THEOREM. 182. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. o Let the figure ABCE be a quadrilateral, having BC equal to AE and AB to EC. To prove that the figure... | |
 | William James Milne - Geometry - 1899 - 398 pages
...quadrilateral is it? 2. How do the opposite angles of a parallelogram compare in size ? Theorem. If Hie opposite sides of a quadrilateral are equal, the figure is a parallelogram. Data: Any quadrilateral, as ABCD, in which AB = DC and AD = BC. To prove ABCD a parallelogram. Proof.... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...PARALLELOGRAMS. 1. If one angle of a parallelogram is a right angle, all its angles are right angles. 2. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 3. If the opposite angles of a quadrilateral are equal, the figure is a parallelogram. , 4. If a quadrilateral... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...rhomboid. PROPOSITION XXXII. THEOREM 195. The opposite sides of a parallelogram are equal; and conversely, if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Ft Let AB CD be a parallelogram. To prove AB = CD and BC = AD. Proof. Draw the diagonal BD. Z1 = Z2.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...equal. Ex. 190. The diagonals of a parallelogram bisect each other. PROPOSITION XXXIII. THEOREM 138. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. DG Hyp. In quadrilateral ABDC AB=CD; AD = BC. To prove ADiBC; AB\ CD. HINT. — Prove the equality... | |
 | Arthur Schultze - 1901 - 260 pages
...equal. Ex. 190. The diagonals of a parallelogram bisect each other. PROPOSITION XXXIII. THEOREM 138. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. D a Hyp. In quadrilateral ABDC AB=CD; AD = BC. To prove AD l BC; AB l CD. HINT.—Prove the equality... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...equal. Ex. 190. The diagonals of a parallelogram bisect each other. PROPOSITION XXXIII. THEOREM 138. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. D c Hyp. In quadrilateral ABDC AB=CD; AD = BC. To prove AD || BC; AB || CD. HINT. — Prove the equality... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...equal by Propositions XXV and IV. Therefore Z BCA = Z DAC, PROPOSITION XXXIII 128. If both pairs of opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given a quadrilateral whose opposite sides are equal. It is required to prove that the opposite sides... | |
 | Education - 1902 - 780 pages
...accepted. First i Define hypothesis, locus of a point, altitude, diamdivision eter> rhomboid. 2 Prove that if the' opposite sides of a quadrilateral are equal, the figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
