## Plane Geometry |

### From inside the book

Results 1-5 of 40

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**circumscribed**about the poly- gon . E A B Ex . 418. Inscribe an equilateral hexagon in a circle ; an equilateral triangle . Ex . 419. The diagonals of an inscribed equilateral pentagon are equal . Ex . 420. If the extremities of any two ... Page 127

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**circumscribed**polygon at their points of tangency pass through a com- mon point . Ex . 438. The line drawn from any vertex of a**circumscribed**polygon to the center of the circle bisects the angle at that vertex and also the angle ... Page 128

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**circumscribed**quadrilat- eral is equal to the sum of the other two sides . Ex . 447. The median of a**circumscribed**trapezoid is one fourth the perimeter of the trapezoid . Ex . 448. A parallelogram**circumscribed**about a circle is either ... Page 129

... quadrilateral . Ex . 453. In triangle ABC , draw XY parallel to BC so that XY + BC = BX + CY . Ex . 454. Inscribe a circle in a given rhombus . PROPOSITION XIV . PROBLEM 323. To

... quadrilateral . Ex . 453. In triangle ABC , draw XY parallel to BC so that XY + BC = BX + CY . Ex . 454. Inscribe a circle in a given rhombus . PROPOSITION XIV . PROBLEM 323. To

**circumscribe**a circle about BOOK II 129. Page 130

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**circumscribed**about an acute triangle ; a right triangle ; an obtuse triangle . Ex . 456 .**Circumscribe**a circle about an isosceles trapezoid . Ex . 457. Given the base of an isosceles triangle and the radius of the**circumscribed**circle ...### Other editions - View all

### Common terms and phrases

acute angle adjacent angles altitude angle formed arc degrees ARGUMENT REASONS assigned value base angles bisector bisects chord circumscribed common measure Construct a triangle diagonals diameter discussion are left divided Draw equal arcs equal circles equal respectively equidistant equilateral triangle equivalent exercise exterior angles figure Find the area Find the locus geometric given circle given line given point given triangle HINT hypotenuse inches included angle inscribed angle intercepted arc isosceles trapezoid isosceles triangle length limit line drawn line joining line of centers mean proportional measure-number median mid-points number of sides obtuse parallel parallelogram perimeter perpendicular prolonged PROPOSITION prove quadrilateral radii radius ratio rectangle regular polygon rhombus right angles right triangle secant segments similar triangles straight line student tangent THEOREM third side trapezoid triangle ABC unequal variable vertex angle vertices

### Popular passages

Page 281 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.

Page 268 - S' denote the areas of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.

Page 76 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 179 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.

Page 95 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.

Page 195 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. 3. In a right triangle the square of either leg is equal to the square of the hypotenuse minus the square of the other leg.

Page 13 - If two angles of a triangle are equal, the sides opposite are equal.

Page 96 - A line joining the midpoints of the non.parallel sides of a trapezoid is parallel to the base, and equal to half the sum of the bases.

Page 64 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 94 - If three or more parallel lines intercept equal segments on one transversal, they intercept equal segments on any other transversal.