## Plane Geometry |

### From inside the book

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**angle**construct a line , limited by the two sides of the**angle**, and ...**inscribed**in another triangle has its sides parallel respectively to the ...**angles**adjacent to either of the non - parallel sides are supplementary . ( c ) ... Page 127

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**angle**at that vertex and also the**angle**between radii drawn to the adjacent ...**angles**of a circumscribed quadrilateral pass through a common point ...**inscribed**in a circle . What kinds of parallelograms are inscriptible ? Ex ... Page 129

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**angles**of a quadrilateral meet at a com- A mon point P , then the line that bisects the remaining**angle**of the quadri- lateral passes through P. ( b ) Tell why a circle can be**inscribed**in this particular quadrilateral . Ex . 453. In ... Page 144

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**angle**is equal to that same multiple of the measure of the**angle**. 363. Def . An**angle**is said to be**inscribed**in a circle if its vertex lies on the circumference and its sides are chords . 364. Def . An**angle**is said to be**inscribed**in ... Page 145

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**inscribed angle**is measured by one half its intercepted arc . B 0 3 2 B 415 B A FIG . 1 . Given inscribed X X FIG . 2 . FIG . 3 . ABC . To prove that ABC ∞ 1⁄2 AC . I. Let one side of Z ABC , as AB , pass through the center of the ...### 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.