## Elements of Plane Geometry |

### From inside the book

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Page 58

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**Trapezoids**, and Parallelograms . 119. A Trapezium is a quadrilateral which has no two of its sides parallel . 120. A**Trapezoid**is a quadrilateral which has two of its sides parallel . The parallel sides are called the bases . 121. A ... Page 59

Franklin Ibach. 125. A Rhombus is an equilateral rhomboid . Trapezium .

Franklin Ibach. 125. A Rhombus is an equilateral rhomboid . Trapezium .

**Trapezoid**. Parallelogram . Rectangle ...**trapezoid**is the perpendicular distance between its bases . PARALLELOGRAMS . THEOREM XL . 128. In any parallelogram ... Page 67

Franklin Ibach. THEOREM XLVII . 140. The parallel to the bases of a

Franklin Ibach. THEOREM XLVII . 140. The parallel to the bases of a

**trapezoid**, bisecting one of the non - parallel sides , bisects the other also . Let ABCD be a**trapezoid**, AB and DC its bases , E the middle point of AD , and let EF be ... Page 131

... equal altitudes are to each other as their bases . 250. COR . 3. - Triangles having equal bases and equal alti- tudes are equivalent figures . THEOREM V. 251. The area of a

... equal altitudes are to each other as their bases . 250. COR . 3. - Triangles having equal bases and equal alti- tudes are equivalent figures . THEOREM V. 251. The area of a

**trapezoid**is equal ELEMENTS OF PLANE GEOMETRY . 131. Page 132

Franklin Ibach. THEOREM V. 251. The area of a

Franklin Ibach. THEOREM V. 251. The area of a

**trapezoid**is equal to half the sum of its parallel sides multiplied by its altitude . Let ABCD be a**trapezoid**, AB and DC its sides , and EF its altitude . D E C A B F To prove that the area ...### Other editions - View all

### Common terms and phrases

AB² ABC and DEF AC and BC acute angle adjacent angles angles are equal angles equals angles formed arc AC BC² bisectors bisects centre CF meet chord common point Concave Polygon construct Convex Polygon COR.-The decagon DEF are similar diagonal BC diameter Draw the diagonal equally distant equals two right equiangular Equilateral Polygon exterior angles given circle given straight line homologous sides hypothenuse included angle intersect La=Lb Let ABCD line joining lines drawn measured by arc medial lines middle point oblique lines parallelogram perimeter PLANE GEOMETRY produced proportion Q. E. D. THEOREM Q. E. F. PROBLEM quadrilateral radii radius rectangle regular inscribed regular polygon respectively equal rhombus right angles right-angled triangle SCHOLIUM secant similar polygons square Subtract tangent third side trapezoid triangles are equal vertex vertical angle

### Popular passages

Page 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.

Page 83 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.

Page 14 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.

Page 136 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.

Page 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.

Page 137 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 177 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.