## A Text-book of Geometry |

### From inside the book

Results 6-10 of 26

Page 61

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**bisect**each other . B C A E Let the figure ABCE be a parallelogram , and let the diagonals AC and BE cut each other at 0 . To prove = AO OC , and BO = OE . In the A AOE and BOC AE = BC , § 168 ( being opposite sides of a ) . LOAE = LOCB ... Page 64

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**bisects**the other side also . For , let DE be I to BC and**bisect**AB . Draw through A a line to BC . Then this line is to DE , by § 111. The three parallels by hypothesis intercept equal parts on the transversal AB , and there- B fore ... Page 72

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**bisects**the vertical angle . 35. State and prove the converse . 36. The bisector of an exterior angle of an isosceles triangle , formed by producing one of the legs through the vertex , is parallel to the base . 37. State and prove the ... Page 73

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**bisect**the angle B , and meet AC in D , show that BD is equal to AD . 54. If from any point in the base of an isosceles triangle parallels to the legs are drawn , show that a parallelogram is formed whose perimeter is constant , and ... Page 77

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**bisects**the circle and the circum- ference . M E B P Let AB be the diameter of the circle AMBP , and AE any other chord . To prove AB > AE , and that AB**bisects**the circle and the circumference . Proof . I. From C , the centre of the O ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē acute angle altitude angles are equal apothem base bisector bisects called centre chord circumference circumscribed circumscribed circle coincide decagon diagonal diameter divide Draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angles feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersect isosceles trapezoid isosceles triangle legs length line joining measured by arc middle points number of sides parallel parallelogram perimeter perpendicular prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 44 - 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 144 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 130 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 211 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 157 - 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 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.

Page 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.