## Plane Geometry: With Problems and Applications |

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ABCD accompanying design acute angle altitude apothem arcs area bounded axes of symmetry axioms bisects central angle chord circle tangent congruent corresponding sides definition diagonal diameter distance divided Draw drawn equal angles equal circles equiangular equilateral triangle EXERCISES exterior angle feet Find the area Find the locus Find the radius fixed point geometric Give the proof given point given segment given triangle Hence hypotenuse inscribed intersection isosceles triangle length line-segment measure meet middle points number of sides Outline of Proof parallel lines parallelogram perimeter preceding proof in full Prove quadrilateral radii ratio rectangle regular dodecagon regular hexagon regular octagon regular polygon regular triangle respectively rhombus right angles right triangle secant semicircle Show shown similar polygons straight angle straight line strip subtend SUGGESTION tangent THEOREM tile trapezoid triangle ABC unit vertex vertices width

### Popular passages

Page 223 - If two triangles have two sides of the one equal to two sides of the other...

Page 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Page 121 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 60 - 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 46 INTERCEPTS BY PARALLEL LINES.

Page 182 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.

Page 161 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 227 - Find the locus of a point such that the difference of the squares of its distances from two fixed points is a constant.

Page 210 - The area of a rectangle is equal to the product of its base and altitude.

Page 31 - Kuclid divided unproved propositions into two classes: axioms, or "common notions," which are true of all things, such as, " If things are equal to the same thing they are equal to each other"; and postulates, which apply only to geometry, such as,