Plane and Solid Geometry

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Charles E. Merrill Company, 1911 - Geometry - 546 pages
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Page 241 - If two triangles have an angle of one equal to an angle of the other, and...
Page 103 - A chord is a straight line joining the extremities of an arc.
Page 54 - Every point in the bisector of an angle is equidistant from the sides of the angle. Hyp. Z DAB = Z DAC and 0 is any point in AD. To prove 0 is equidistant from AB and AC. Draw OP _L AB and OP' _L AC, and prove the equality of the two triangles.
Page 82 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 114 - In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the center, and the greater chord is at the less distance.
Page 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 416 - Every section of a circular cone made by a plane parallel to the base is a circle. Let the section abcd of the circular cone S-ABCD be parallel to the base. To prove that abcd is a circle.
Page 35 - The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line...
Page 193 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 450 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. Given the spherical triangle ABC, with angle B equal to angle C. To prove that AC = AB. Proof. Let A A'B'C ' be the polar triangle of A ABC.

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