## Elements of Plane Geometry |

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ABC and DEF ABCD altitudes angle formed Apply base bisector bisects called chord circle circum circumference circumscribed common consequent Construct contains CONVERSELY COROLLARY DEFINITION diagonals diameter difference divided Draw drawn EFGH equally distant equiangular equilateral triangle equivalent EXERCISE exterior angles externally extremities figure Find four given circle given line given point greater half homologous hypotenuse included intercepted interior isosceles triangle length less Let ABC limit line joining mean medians meet middle points opposite sides parallel parallelogram passes perimeter perpendicular point of intersection polygon prolonged Proof proportion PROPOSITION Prove quadrilateral radii radius ratio rectangle Required respectively right angles right-angled triangle secants segments Show sides similar square straight line Suggestion tangent THEOREM third trapezoid triangle ABC unequal vertex Whence

### 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.