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" An exterior angle of a triangle is equal to the sum of the two opposite interior angles. "
Junior High School Mathematics ... - Page 29
by Edson Homer Taylor, Fiske Allen - 1923
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...of the third side. 136. Theorem. The sum of the angles of a triangle is equal to 180 degrees. 137. Corollary. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. 138. Corollary. The sum of the acute angles of a right triangle is equal to 90 degrees. 139. Corollary....
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...COR. I. It follows from the above demonstration that Z BCD = Z ECD + Z BCE = Z A + Z 7?; hence, 1. Jre exterior angle of a triangle is equal to the sum of the two opposite interior angles. 2. An exterior angle of a triangle is greater than either of the opposite interior angles. 85. COE....
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...perimeter of a triangle is less than twice the sum of the medians. PROPOSITION XXVIII. 119. Theorem. An exterior angle of a triangle is equal to the sum of the opposite interior angles. Let ABC represent a triangle, D AC an exterior angle, and В and С the...
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Proceedings of the Board of Public Instruction of the City of Albany, Volume 15

Albany (N.Y.). Board of Public Instruction - Education - 1895 - 620 pages
...How many degrees in the angle formed by the hands of a clock at four o'clock ? 10-12. Prove that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. 13-15. Prove that if one of the acute angles of a right triangle is double the other, the hypotenuse...
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Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - Education - 1895 - 686 pages
...multiplied by the apothegm. 9. Demonstrate: The exterior angle formed by producing one of the Bides of a triangle, is equal to the sum of the two opposite interior angles. 10. Demonstrate: If two angles have two sides parallel and extending in the same direction with each...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...interior angles. Can you give a reason for the fact stated in the following theorem ? PJRINCIPLE 20. — An exterior angle of a triangle is equal to the sum of the opposite interior angles. 71. Find angle c and angle b. 72. Every degree is divided into 60 equal...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 382 pages
...(47) 121. COB. 1. Each angle of a triangle is the supplement of the sum of the other two. 122. COR. 2. An exterior angle of a triangle is equal to the sum of the two remote interior angles. For its supplement is also the supplement of those two. 123. COR. 3....
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 706 pages
...6. Construct a right-angled triangle, having given one side and the angle opposite. PROPOSITION 32. An exterior angle of a triangle is equal to the sum of the two interior opposite angles ; and the sum of the three interior angles of a triangle is equal...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...AC and AE. To PROVE — angle m is measured by \ (arc CE — arc BD). Join CD. Then m + w=s. 59 [An exterior angle of a triangle is equal to the sum of the two opposite interior angles.] Hence m = s—w. Ax. 3 But s is measured by i arc CE. 197 And w is measured by arc BD. 197...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...secants, AC and AE. To PROVE — angle m is measured by ^ (arc CE— arc BD). Join CD. Then m -\-ws. 59 [An exterior angle of a triangle is equal to the sum of the two opposite interior angles.] Hence m = s — tv. But s is measured by arc CE. And w is measured by \ arc BD. Hence m is measured...
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