## Plane Geometry |

### From inside the book

Results 1-5 of 37

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**quadrilateral**and produce the sides beyond the vertices . How many exterior angles are formed ? How many pairs of vertical angles ? 2. Answer the same questions for polygons of 5 , 6 , 7 , 8 , 9 , 10 , n sides . 3. How many diagonals ... Page 50

... 8. Construct the sum of the angles of a

... 8. Construct the sum of the angles of a

**quadrilateral**. 9. Construct the sum of three consecutive angles of a regular hexagon . COMPUTATIONS 10. How many degrees in a quadrant ? 11. 50 PLANE GEOMETRY - PRELIMINARY COURSE. Page 51

... , show that each triangle is but a repetition of the other . Under what circumstances can a circle be circumscribed about the entire figure ? B A α a b b C 22. Inscribe a

... , show that each triangle is but a repetition of the other . Under what circumstances can a circle be circumscribed about the entire figure ? B A α a b b C 22. Inscribe a

**quadrilateral**in a circle . Construct the EXERCISES 51. Page 52

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**quadrilateral**( see accom- panying figure ) such that Za + 2b + c = 2 rt . 6 . 29. How many of the geometric ideas developed so far do you find illustrated con- cretely in the schoolroom ? n m a X b a b C 30. Prepare a summary of the ... Page 55

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**quadrilateral**A'B'C'D ' so that A'B'C'D ' | ABCD . 4. Place a plane mirror so that it is perpendicular to a sheet of paper . Mark a point on the paper . Observe that the point and its image are symmetrically situated with respect to the ...### 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.