 | Euclid - Euclid's Elements - 1904 - 488 pages
...PARALLELOGRAMS. i. 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... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...sides of a quadrilateral are equal and parallel, then the other two sides are equal and parallel, and the figure is a parallelogram. Let the figure ABCE be a quadrilateral, having the side AE equal and parallel to BC. To prove that AB is equal and parallel to EC. Proof. Draw AC.... | |
 | William Chauvenet - 1905 - 336 pages
...opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. PROPOSITION XXXI. If the opposite sides of a quadrilateral are equal, the figure Is a varallelogram. PROPOSITION XXXII. The diagonals of a parallelogram bisect each other. BOOK II. PROPOSITIONS.... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...equal. SUGGESTION.— Show that in any rectangle A BCD the triangle ABC= triangle AB D. 3. Show that if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. SUGGESTION.— Draw the diagonal. Then, by Art. 75, the triangles formed are equal. 4. Show that if... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...equal triangles. 133. COR. The opposite angles of a parallelogram are equal. (See 27.) 134. THEOREM. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. [Converse of 130.] Given: Quadrilateral AB CD; AB = DC ; AD = BC. To Prove : ABCD is a O. Proof : Draw... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...triangles. 202 COROLLARY 2. Parallels comprehended between parallels are equal. PROPOSITION XXX. THEOREM 204 If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. HYPOTHESIS. ABCD is a quadrilateral, having AD = BC and AB = DC. CONCLUSION. ABCD is a parallelogram.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...triangles. 202 COROLLARY 2. Parallels comprehended between parallels are equal. PROPOSITION XXX. THEOREM 204 If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. HYPOTHESIS. ABCD is a quadrilateral, having AD = BC and AB = DC. CONCLUSION. ABCD is a parallelogram.... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...equal triangles. 133. COR. The opposite angles of a parallelogram are equal. (See 27.) 134. THEOREM. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. [Converse of 130.] Given: Quadrilateral ABCD; A, AB — DC ; AD = BC. To Prove : ABCD is a O. / Proof... | |
 | University of Oxford - 1907 - 160 pages
...having given the base, one of the angles at the base, and the sum of the remaining 5. (£>) Show that if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 6. In the triangle ABC, AB is equal to AC and BD is drawn perpendicular to AC cutting AC in D. Show... | |
 | Henry Sinclair Hall - 1908 - 286 pages
...AOB = vert. opp. /.COD, and AB = the opp. side CD ; .'. OA=OC; and OB = OD. Theor. \T. EXERCISES. 1. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 2. If the opposite angles of a quadrilateral are equal, the figure is a parallelogram: 3. If the diagonals... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
