## Plane Geometry |

### From inside the book

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**Rhombus**is a parallelogram having two adjacent sides equal . It can be proved and it is important to remember that all the sides of a**rhombus**are equal ; also it is usually implied that the angles are not right angles . ( See § 143 ... Page 74

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**rhombus**. Hence every theorem true about a rectangic or a**rhombus**is true about a square . ( See Note , § 141. ) 144. Many artistic designs are made on a network of squares as illustrated below . G CORNER AND BORDER PPPPH 名 4 XXXXXX ... Page 75

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**rhombus**. Ex . 161. How large are the angles into which a diagonal of a square divides its angles ? Ex . 162 . Ex . 163 . Construct a square whose diagonals shall be 2 in . in length . Prove that the lines drawn from the ends of one ... Page 92

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**rhombus**. Ex . 213. If the lower base AD of trapezoid ABCD is double the upper base BC , and the diagonals intersect at E , prove that CE is AE and that BE is ED . ( § 152. ) Ex . 214. If D is any point in side AC of △ ABC and E , F ... Page 136

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**rhombus**having given its base and altitude . Ex . 145. Construct a right triangle having given the hypotenuse and the length of the altitude upon it . Ex . 146 . Construct an isosceles triangle having given the base and the angle ...### Other editions - View all

### Common terms and phrases

ABCD acute angle adjacent angles adjoining figure altitude angles are equal apothem base bisector bisects central angle chord circle of radius circumscribed polygons Conclusion congruent Construct a triangle Determine diagonals diameter divide Draw drawn equal angles equal circles equal respectively equal sides equidistant equilateral triangle extended exterior angle geometry given circle given point given segment given triangle Hence homologous sides hypotenuse Hypothesis intersect isosceles trapezoid isosceles triangle length mean proportional median meeting AC mid-point Note number of sides opposite sides parallel parallelogram pentagon perigon perimeter perpendicular perpendicular-bisector PROPOSITION quadrilateral radii ratio rectangle regular inscribed polygons regular polygon rhombus right angle right triangle secant similar triangles straight angle straight line Suggestion Suggestions.-1 Supplementary Exercises tangent THEOREM trapezoid triangle ABC triangle equal Try to prove vertex ZAOB

### Popular passages

Page 166 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Page 207 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 166 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Page 83 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.

Page 170 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 105 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 86 - If two triangles have two sides of one equal, respectively, to two sides of the other...

Page 204 - 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 299 - Prove that an equiangular polygon inscribed in a circle is regular if the number of sides is odd. Ex.

Page 194 - Two rectangles are to each other as the products of their bases and altitudes. For if R = a6, and R