## Plane GeometryMacmillan, 1901 |

### From inside the book

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**Similar Polygons**Book IV . Areas of Polygons Book V. Regular Polygons . Measurement of the Circle APPENDIX TO PLANE GEOMETRY Algebraic Solutions of Geometrical Propositions Maxima and Minima . PAGE 1 9 73 118 164 0 194 217 225 SYMBOLS ... Page 13

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**Similar**abbreviations will be suggested for other propositions . 71. DEF .**Polygons**are mutually equiangular if their angles are respectively equal , and mutually equilateral if their sides are respectively equal . If two**polygons**are ... Page 117

... . To find a point , X , in CD , such that AXC = LBXD . Ex . 516. The bisectors of the angles of a circumscribed quadrilateral meet in a point . BOOK III PROPORTION .

... . To find a point , X , in CD , such that AXC = LBXD . Ex . 516. The bisectors of the angles of a circumscribed quadrilateral meet in a point . BOOK III PROPORTION .

**SIMILAR POLYGONS**255. A proportion is MISCELLANEOUS EXERCISES 117. Page 118

... The two terms of a ratio must be either quantities of the same kind , or the quantities must be represented by their numerical measures only . PROPOSITION I. THEOREM 262. In any proportion , the product 118 Proportion

... The two terms of a ratio must be either quantities of the same kind , or the quantities must be represented by their numerical measures only . PROPOSITION I. THEOREM 262. In any proportion , the product 118 Proportion

**Similar Polygons**. Page 119

... both members by np m p - 2 . n Q.E.D. Ex . 519. If ab = mn , find all possible proportions consisting of a , b , m , and n . PROPOSITION III . THEOREM 266. A mean proportional between two PROPORTION .

... both members by np m p - 2 . n Q.E.D. Ex . 519. If ab = mn , find all possible proportions consisting of a , b , m , and n . PROPOSITION III . THEOREM 266. A mean proportional between two PROPORTION .

**SIMILAR POLYGONS**119.### Other editions - View all

### Common terms and phrases

AABC ABCD adjacent angles algebraic altitude angle equal angle formed angles are equal apothem base angle bisect bisector central angle circumference construct a triangle decagon diagonals diagram for Prop diameter draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle find a point Find the area given circle given line given point given triangle HINT homologous sides hypotenuse inscribed isosceles triangle joining the midpoints line joining mean proportional measured by arc median opposite sides parallel lines parallelogram perimeter perpendicular perpendicular-bisector point equidistant produced proof is left PROPOSITION prove Proof proving the equality quadrilateral radii rectangle regular hexagon regular polygon rhombus right angle right triangle SCHOLIUM School secant segments side equal similar polygons similar triangles straight angle straight line tangent THEOREM third side transversal trapezoid triangle ABC triangle are equal vertex vertical angle

### Popular passages

Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 180 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 31 - The median to the base of an isosceles triangle is perpendicular to the base.

Page 209 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.

Page 130 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 71 - The midpoints of two opposite sides of a quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex.

Page 26 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.

Page 190 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 56 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.