## Plane Geometry |

### From inside the book

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**intercepted**by equal central angles . B 86. If in the previous figures we had drawn the chords subtending the arcs AB , BC , etc. , we could have proved at the same time that the equality of the arcs involves also the equality of 0 A ... Page 48

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**intercepted**by equal central angles . 3. Equal chords subtend equal arcs . 4. Equal arcs are subtended by equal chords . RESULTING CONSTRUCTIONS 89. Construction IV . To construct an angle equal to a given angle . B A B. Ө. A ' B 0 A B A ... Page 50

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**intercepted**arc . In other words , 94. A central angle is measured by its**intercepted**arc . 95. Regular Polygons . The chords of the arcs**intercepted**by equal central angles of a circle are equal . Also the base angles of the isosceles ... Page 87

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**intercepted**by the arc . The line which bisects this angle will , if produced , bisect the given arc also . EXERCISES Why ? 1. Construct a scalene triangle and draw the bisectors of the inte- rior angles , producing each to meet the ... Page 143

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**intercepted**arc ( § 94 ) . 9. In the same circle , or in equal circles , the greater central angle**intercepts**the greater arc , and the greater arc is inter- cepted by the greater central angle ( § 94 ) . 10. A diameter of a circle ...### Common terms and phrases

ABCD acute angle altitude angles are equal base angles bisects called central angle chord circumscribed polygon congruent COROLLARY determined diagonals diameter distance divided Draw drawn equal angles equilateral triangle EXERCISES exterior angles figure Find the area Find the length geometry given circle given line given point Given the triangle given triangle Hence homologous homologous sides hypotenuse intercepted interior interior angles isosceles trapezoid isosceles triangle joining legs line-segment locus measured method mid-points number of sides obtuse octagon opposite sides parallelogram perimeter perpendicular bisector plane point equidistant PROBLEM produced Proof PROPOSITION protractor prove quadrilateral radii radius ratio rectangle regular inscribed polygon regular polygon rhombus right angle right triangle round angle segment semicircle Show similar triangles straight angle straight line subtended tangent THEOREM third side trapezoid triangle ABC vertex angle vertices

### Popular passages

Page 247 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Page 79 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 293 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 207 - If two triangles have an angle of one equal to an angle of the other, and...

Page 151 - In the same circle, or in equal circles, if two chords are unequally distant from the center, they are unequal, and the chord at the less distance is the greater.

Page 131 - ... the third side of the first is greater than the third side of the second.

Page 257 - If two chords intersect within a circle, the product of the segments of one chord is equal to the product of the segments of the other.

Page 105 - A line drawn from the vertex of the right angle of a right triangle to the middle point of the hypotenuse divides the triangle into two isosceles triangles.

Page 138 - The medians of a triangle meet in a point which is two thirds of the distance from each vertex to the middle of the opposite side.

Page 119 - If three or more parallels intercept equal parts on one transversal, they intercept equal parts on every transversal. Given the parallels AB, CD, and EF intercepting equal parts on the transversal MN.