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" If two parallel lines are cut by a transversal, the corresponding angles are equal. "
Third-year Mathematics for Secondary Schools - Page 339
by Ernst Rudolph Breslich - 1917 - 369 pages
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...I. ^/4 + ^6=^5+^3. Why ? 2. Compare Z.?, 6 and 5. Therefore — PROPOSITION XXII. 112. Theorem. // two parallel lines are cut by a transversal, the corresponding angles are equal. Let С D and EF represent two parallel lines, cut by the transversal AB. To prove that the corresponding...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...lines ; prove that the second straight line is bisected by the first. Proposition 28. Theorem. 39. If two parallel lines are cut by a transversal, the corresponding angles are equal. Consult Prop. 27 and Prop. 6. Ex. 34. If two parallel lines are cut by a transversal, the alternate...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...the opposite sides of a quadrilateral are parallel, they must be equal. PROPOSITION IX. THEOREM 89. If two parallel lines are cut by a transversal, the corresponding angles are equal. [Converse of Prop. VI.] •EHyp. Two parallel lines CD and EF are intersected by AB in H and /, respectively....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...the opposite sides of a quadrilateral are parallel, they must be equal. PROPOSITION IX. THEOREM 89. If two parallel lines are cut by a transversal, the corresponding angles are equal. [Converse of Prop. VI.] ~BJi Hyp. Two parallel lines CD and EF are intersected by AB in H and /, respectively....
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...the opposite sides of a quadrilateral are parallel, they must be equal. PROPOSITION IX. THEOREM 89. If two parallel lines are cut by a transversal, the corresponding angles are equal. [Converse of Prop. VI.] Zf. JS Hyp. Two parallel lines CD and EF are intersected by AB in H and I,...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...the opposite sides of a quadrilateral are parallel, they must be equal. PROPOSITION IX. THEOREM 89. If two parallel lines are cut by a transversal, the corresponding angles are equal. [Converse of Prop. VI.] TS-D Hyp. Two parallel lines CD and EF are intersected by AB in // and /, respectively....
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...parallel lines are cut by a transversal, the alternate-interior angles are equal. 53. Theorem XVII. If two parallel lines are cut by a transversal, the corresponding angles are equal.. 54. Corollary. If two parallel lines are cut by a transversal, the alternate-exterior angles are equal....
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Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...+ Z.6 = Z.$ + -^ 3. Why ? 2. Compare .^s 6 and 5. Therefore — PROPOSITION XXII. 112. Theorem. // two parallel lines are cut by a transversal, the corresponding angles are equal. Let CD and EF represent two parallel lines, cut by the transversal AB. To prove that the corresponding...
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First-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Mathematics - 1909 - 402 pages
...compare the corresponding angles. 196. Exercises 7 and 8 illustrate the following theorem: Theorem: // two parallel lines are cut by a transversal the corresponding angles are equal. EXERCISES 1. Two parallels and a transversal make angles designated as shown in Figs. 120, 121. Find...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...transversal on which the sum of the angles is less than a straight angle. PROPOSITION XXXIII. THEOREM. 148. If two parallel lines are cut by a transversal, the corresponding angles are equal. B Given the II lines AB and CD, cut by EH in F and G, respectively. To prove % BFE = % DGF. Proof....
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