## Plane GeometryMacmillan, 1901 |

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### Common terms and phrases

ABCD adjacent angles algebraic altitude angle equal angle formed angles are equal apothem base angle bisector bisects central angle circumference circumscribed construct a triangle decagon diagonals diagram for Prop diameter draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle find a point Find the area given circle given line given point given triangle HINT homologous sides hypotenuse inscribed intersecting isosceles triangle joining the midpoints line joining mean proportional median opposite sides parallel lines parallelogram perimeter perpendicular perpendicular-bisector point equidistant produced proof is left PROPOSITION prove Proof proving the equality quadrilateral radii rectangle regular hexagon regular polygon rhombus right angle right triangle SCHOLIUM School secant segments side equal similar polygons similar triangles straight angle straight line tangent THEOREM third side transversal trapezoid triangle ABC triangle are equal vertex vertical angle

### Popular passages

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 180 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.

Page 31 - The median to the base of an isosceles triangle is perpendicular to the base.

Page 152 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 143 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.

Page 131 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 14 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.

Page 26 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.