## Plane Geometry |

### From inside the book

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**equal to twice as many right angles as the figure has sides**, less four right angles . B A C E Appl . Prove A + B + C , etc. = - ( 2 n − 4 ) rt . Cons . Draw diagonals from one vertex . Let n the number of sides Dem . - n 2 = no . of A ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē acute angle ADē adjacent angles angles are equal apothem Appl base angle bisector bisects central angle centre chords circumference circumscribed circle coincidence Cons construct decagon degrees diagonals diameter dist distance divided equal circles equally distant equiangular equiangular polygon equilateral triangle equivalent EXERCISES exterior angle feet figure Find the area geometric given circle given point hexagon homologous sides hypotenuse INTERPRET AND PROVE intersecting isosceles trapezoid isosceles triangle line drawn locus logarithm mantissa mean proportional meas measure median middle point number of sides parallel parallelogram perimeter perpendicular produced PROPOSITION quadrilateral radius ratio rectangle regular polygon respectively rhombus right angle right triangle secant segments similar polygons square subs subtended tang tangent Theorem third side trapezoid triangle ABC triangles are equal variable vertex vertical angle ΙΟ

### 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.