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" In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 56
by Nathan Scholfield - 1845
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School Science and Mathematics, Volume 11

Education - 1911 - 946 pages
...important ways. In teaching certain propositions in geometry, such for instance as the theorem that in the same circle or in equal circles equal arcs are subtended by equal chords, I have often noticed that even though the pupil at the outset of the demonstration had a clear grasp...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - Geometry - 1905 - 50 pages
...Def. 45. The straight line joining any two points on a circumference is called a chord. Prop. 18. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Prop. 19. In the same circle, or in equal circles, equal chords subtend equal arcs. to the middle point...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...point B on M (?) (201). Arc AB will coincide with arc LM (?) (192). .-. AB = LM (?) (28). QED 207. THEOREM. In the same circle (or in equal circles) equal arcs are intercepted by equal central angles. [Converse.] Given : OO = OC;arc.4B = arc LM. To Prove : Z o =...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...and point B on M (?) (201). Arc AB will coincide with arc LM (?) (192). ...AB = LM (?) (28). QED 207. THEOREM. In the same circle (or in equal circles) equal arcs are intercepted by equal central angles. [Converse.] Given : OO = OC ; arc AB = arc LM. To Prove : ZO =...
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Second-year Mathematics for Secondary Schools, Volume 2

George William Myers - Mathematics - 1910 - 304 pages
...form unequal angles intercept unequal arcs on the circumference, and conversely. PROPOSITION XXVI 95. Theorem: In the same circle or in equal circles, equal...arcs are subtended by equal chords, and conversely. I. Given circle O, with arc AB=arc CD (Fig. 63). FIG. 63 To prove chord AB =chord C D. This is left...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...or in equal circles, sectors with equal central angles are equal. PROPOSITION II. THEOBEM. 233. In the same circle, or in equal circles, equal arcs are subtended ~by equal chords and intercepted by equal central angles. Given OC = O C' and arc AB = arc A'B'. To prove chord AB= chord...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...Cf, and ZC coincides with Z c'. Then A falls on A' and B on B'. (§ 189) Hence AB = AW. (§ 196) 200. THEOREM. In the same circle or in equal circles equal arcs are intercepted by equal central angles. Given QC=QC,AB = A'ff. (See figure, § 199.) To prove that Z c=...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...and Z. C coincides with Z C'. Then A falls on A1 and B on B'. (§ 189) Hence AB = A!B'. (§ 196) 200. THEOREM. In the same circle or in equal circles equal arcs are intercepted by equal central angks. Given OC = OC, AB = A'ff. (See figure, § 199.) To prove that Z....
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Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...circumference. The circle is then said to be circumscribed about the polygon. PROPOSITION II. THEOKEM 177. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, 0 and 0', Proof. Draw radii, OA, OB, O'A', O'B'. Z AOB = Z A'O'B', (equal arcs subtend...
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School Work, Volume 3

Education - 1904 - 484 pages
...This and similar exercises may be assigned as home work. EXERCISE 79. Show by superposition that in the same circle, or in equal circles, equal arcs are subtended by equal chords; that equal chords are equidistant from the centre. After following the directions of the above in several...
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