## Elements of Plane Geometry |

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### Common terms and phrases

AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc AC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point hexagon homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ

### Popular passages

Page 68 - 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.

Page 163 - 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 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.

Page 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.

Page 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.

Page 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...

Page 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.

Page 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.