## Plane Geometry |

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### Common terms and phrases

AB² ABCD AC² acute angle AD² adjacent angles altitude angles are equal apothem Appl base and altitude base angle BC² BD² bisector bisects central angle centre chord circumf circumference circumscribed circle Cons decagon diagonals diameter dist distance divided Draw equal circles equally distant equiangular equiangular polygon equilateral triangle EXERCISES exterior angle feet figure Find its area Find the area geometric given circle given line given point homologous sides hypotenuse intersecting isosceles trapezoid isosceles triangle length locus logarithm mantissa mean proportional meas measure median middle point number of sides parallel parallelogram perimeter perpendicular Problem produced PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon respectively rhombus right angle right triangle secant segments similar triangles subtended tang tangent Theorem third side trapezoid triangle ABC triangles are equal vertex vertical angle

### Popular passages

Page 60 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.

Page 219 - ... 4. Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.

Page 139 - 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 44 - 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 43 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 217 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.

Page 89 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 107 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 218 - 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'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 218 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.