## Elements of Plane Geometry |

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### Common terms and phrases

ABē ABC and A'B'C ACē adjacent angles altitude angle formed angles are equal arc A'B base bisects central angle circumcenter circumscribed circle decagon diagonals diameter Draw drawn equal circles equiangular equiangular polygon equilateral triangle exterior Find the area geometry given circle given line given point Given the line greater Hence homologous sides hypotenuse inscribed circle inscribed regular interior angles intersecting isosceles triangle legs line joining measured by arc median number of sides orthocenter parallel parallelogram perigon perimeter points equidistant produced prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively rhombus right angle right triangle secant segments similar polygons square straight angle straight line tangent THEOREM third side trapezoid triangle ABC triangle are equal triangles are congruent vertex vertical angle

### Popular passages

Page 41 - 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 42 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 243 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R

Page 179 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 62 - 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 5 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.

Page 135 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 67 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.

Page 176 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.

Page 21 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.