# Plane Geometry, with Problems and Application

Creative Media Partners, LLC, 1918 - Mathematics - 332 pages
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### Popular passages

Page 208 - The square of the bisector of an angle of a triangle is equal to the product of the sides of this angle diminished by the product of the segments made by the bisector upon the third side of the triangle.
Page 205 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 104 - A, from A to B, from B to C, and from C to...
Page 207 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 85 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 220 - Euclidean geometry, it is logically necessary that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
Page 261 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 209 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 34 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 115 - If the straight lines bisecting the angles at the base of an isosceles triangle be produced to meet, show that they contain an angle equal to an exterior angle at the base of the triangle. tEx.