 | Euclid - Geometry - 1892 - 460 pages
...EXERCISES. 1. If one angle of a parallelogram is a right angle, all its angles arc 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 Ji9ure ii a parallelogram. •i. If a quadrilateral... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...figure ABCE is a O, § 168 (the opposite sides being parallel). QE a PROPOSITION XL. THEOREM. 183. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram,. Q Let the figure ABCE be a quadrilateral having BC = AE and AB = EC. To prove figure ABCE a O. Proof.... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...equal, the lines are parallel). .-. the figure ABCE is a O, § 168 PROPOSITION XL. THEOREM. 183. If tlw opposite sides of a quadrilateral are equal, the figure is a parallelogram. C Let the figure ABCE be a quadrilateral having BG = AE and AB = EC. To prove figure ABCE a O. Proof.... | |
 | William Chauvenet - 1893 - 340 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 parallelogram. PROPOSITION XXXII. The diagonals of a parallelogram bisect each other. BOOK II. PROPOSITIONS. POSTULATE.... | |
 | Paul Henry Hanus - Geometry - 1893 - 76 pages
...equal triangles. Opposite sides are equal. Opposite angles are equal. Diagonals bisect each other. If the opposite sides of a quadrilateral are equal, the figure is parallelogram. 3. The Trapezoid. Construct trapezoids of different shapes. Angles in every trapezoid.... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
............ (110) Z ADC '= Z ABC + Z BCD ...... (137) .-.AACBis> AABC+Z.BCD ..... (110) EXAMPLE 2. Prove that if the opposite sides of a quadrilateral are equal the figure is a parallelogram. HYPOTHESIS. In quadrilateral A BCD, AB = CD, BC = AD. CONCLUSION. ABCD is a a. Proof. Draw AC. In the... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...parallel, then the other two sides are equal and parallel, and the figure is a parallelogram. 183. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 184. The diagonals of a parallelogram bisect each other. 185. Two parallelograms, having two sides... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...everywhere equally distant. [Fig- 2.] Hint. -Apply §§ 33, 36, 118. PROPOSITION XXXVI. THEOREM 120. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. To PROVE the quadrilateral is a parallelogram. GIVEN — any quadrilateral having its opposite sides... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...everywhere equally distant. [Fig. 2.] Hint.— Apply §§ 33, 36, 118. PROPOSITION XXXVI. THEOREM 120. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. GIVEN—any quadrilateral having its opposite sides equal, viz.: AB = CD, and AD = BC. To PROVE the... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...are its legs, and if the legs are equal the trapezoid is isosceles. PROPOSITION XXVII 108. Theorem. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Appl. 1 = 1, 11 = 11. Prove ABCD = O Cons. Draw BD Dem. A= [3s. = 3s.] .-.1=2 T 1 3 = 4 LJ homol. parts... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
