Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página vii
... Chords , and Secants 95 Summary of Chapter II 106 Problems and Applications 107 CHAPTER III . Measurement of Straight Line - segments . Approximate Measurement Ratios of Line - segments Theorems on Proportional Segments . 112 114 116 ...
... Chords , and Secants 95 Summary of Chapter II 106 Problems and Applications 107 CHAPTER III . Measurement of Straight Line - segments . Approximate Measurement Ratios of Line - segments Theorems on Proportional Segments . 112 114 116 ...
Página 84
... chord . A chord which passes through the center is a diameter . CHAPTER II . STRAIGHT LINES AND CIRCLES . 180. A circle ( § 12 ) divides the plane into two parts such that any point which does not lie on the circle lies within it or ...
... chord . A chord which passes through the center is a diameter . CHAPTER II . STRAIGHT LINES AND CIRCLES . 180. A circle ( § 12 ) divides the plane into two parts such that any point which does not lie on the circle lies within it or ...
Página 85
... chord which joins its end - points . Evi- dently every chord of a circle subtends two arcs . Unless otherwise indicated the arc subtended by a chord means the minor arc . 185. An angle formed by two radii is called a central angle . An ...
... chord which joins its end - points . Evi- dently every chord of a circle subtends two arcs . Unless otherwise indicated the arc subtended by a chord means the minor arc . 185. An angle formed by two radii is called a central angle . An ...
Página 87
... chords , and conversely . 2. Can two intersecting circles have the same center ? 3. From a point on a circle construct two equal chords . 4. Show that the bisector of the angle formed by the chords in Ex . 3 passes through the center of ...
... chords , and conversely . 2. Can two intersecting circles have the same center ? 3. From a point on a circle construct two equal chords . 4. Show that the bisector of the angle formed by the chords in Ex . 3 passes through the center of ...
Página 88
... chord of a circle . 6. Show that the two arcs into which the extremities of a diameter divide a circle are equal ; that is , each is a semicircle . SUGGESTION . Fold the figure over on the diameter . 7. Show that by bisecting the angles ...
... chord of a circle . 6. Show that the two arcs into which the extremities of a diameter divide a circle are equal ; that is , each is a semicircle . SUGGESTION . Fold the figure over on the diameter . 7. Show that by bisecting the angles ...
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Términos y frases comunes
ABCD acute angle adjacent angles altitude angle formed angles are equal apothem axes of symmetry axioms base bisects called central angle chord circle tangent circumscribed coincide congruent corresponding sides Definition diagonal diameter distance divided dodecagon Draw drawn equal angles equal circles equiangular equilateral triangle EXERCISES exterior angle figure Find the area Find the locus Find the radius fixed point geometric Give the proof given point given segment given triangle Hence hypotenuse hypothesis inches inscribed intersection isosceles trapezoid isosceles triangle l₁ length line-segment measure meet middle points number of sides Outline of Proof parallel lines parallelogram perigon perimeter plane proof in full quadrilateral radii ratio rectangle regular hexagon regular octagon regular polygon rhombus right angles right triangle secant semicircle Show shown square straight angle straight line subtend SUGGESTION THEOREM trapezoid triangle ABC vertex vertices width
Pasajes populares
Página 223 - If two triangles have two sides of the one equal to two sides of the other...
Página 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 121 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Página 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.
Página 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.
Página 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.
Página 227 - Find the locus of a point such that the difference of the squares of its distances from two fixed points is a constant.
Página 210 - The area of a rectangle is equal to the product of its base and altitude.
Página 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,