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Geometric Proof

Geometric Proof. Prove that the sum of the angles in a triangle is 180 ˚. x. x. x. y. y. y. a. a. Draw a line parallel to one side. Let x and y be the other two angles formed with the line. b. b. c. c. Then x = b (alternate angles). and y = c (alternate angles).

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Geometric Proof

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  1. Geometric Proof Prove that the sum of the angles in a triangle is 180˚. x x x y y y a a Draw a line parallel to one side. Let x and y be the other two angles formed with the line. b b c c Then x = b (alternate angles) and y = c (alternate angles) We can also see that x + y + a = 180˚. (angles on a line) Therefore, a + b + c = 180˚.

  2. Prove that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. Let the exterior angle be x. a We must show that a + b = x. Let the other interior angle be c. x b c We know that a + b + c = 180˚. (angles in a triangle) We also know that x + c = 180˚. (angles on a straight line) Therefore, a + b = x.

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