## A Text-book of Geometry |

### From inside the book

Results 1-5 of 20

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**bisects**the P straight line which joins them . Thus , C + FIG 22 P P and P ' are symmetrical with respect to C as a centre , if C**bisects**the straight line PP ' . 61. Two points are said to be sym- metrical with respect to a straight ... Page 14

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**bisects**every straight line drawn through it and terminated by the boundary of the figure . 65. A plane figure is symmetrical with respect to a straight line , if the line divides it into two parts , which are sym- metrical with respect ... Page 27

... vertical angles

... vertical angles

**bisects**the other . Ex . 7. The bisectors of the two pairs of vertical angles formed by two intersecting lines are perpendicular to sech other 109. If two parallel lines are cut by a thir PROPOSITION XI . THEOREM . Page 48

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**bisect**the B In the ADB and ADC , AB = AC . AD = AD , L BAD = L CAD . ..A ADB A ADC , = ( two are equal if two sides and the ...**bisects**the angle at the vertex . 156. If two angles of a triangle are equal , PROPOSITION XXIX . THEOREM . Page 63

... ( each having a side and two adj . 4 respectively equal to a side and two adj . of the others ) . .. AB BC = CD , ( homologous sides of equal △ ) . Q. E. D. D bisecting one side ,

... ( each having a side and two adj . 4 respectively equal to a side and two adj . of the others ) . .. AB BC = CD , ( homologous sides of equal △ ) . Q. E. D. D bisecting one side ,

**bisects**the other side also PROPOSITION XLIII . THEOREM .### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 46 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...

Page 69 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.

Page 187 - Two triangles having 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.

Page 64 - 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.

Page 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 215 - 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 161 - 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 135 - 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 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

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.