## A Text-book of Geometry |

### From inside the book

Results 6-10 of 49

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**perpendicular**, and only one , can be drawn from P to AB . Proof . Turn the part of the plane above AB about AB as an axis until it falls upon the part below AB , and denote by P ' the position that P takes . Turn the revolved plane ... Page 22

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**perpendicular**to AC . To prove AB and CD parallel . Proof . If AB and CD are not parallel , they will meet if sufficiently prolonged , and we shall have two**perpendicular**lines from their point of meeting to the same straight line ; but ... Page 23

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**perpendicular**to one of two parallel lines , it is**perpendicular**to the other . H A- M E Ο -B N F K Let AB and EF be two parallel lines , and let HK be**perpendicular**to AB . To prove HKL EF . Proof . Suppose MN drawn through C1 to HK ... Page 26

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**perpendicular**to the bisector , this line forms equal angles with the sides of the given angle . Ex . 5. If the bisectors of two adjacent angles are**perpendicular**to each other , the adjacent angles are supplementary . PROPOSITION XI ... Page 27

... vertical angles bisects the other . Ex . 7. The bisectors of the two pairs of vertical angles formed by two intersecting lines are

... vertical angles bisects the other . Ex . 7. The bisectors of the two pairs of vertical angles formed by two intersecting lines are

**perpendicular**to each other . PROPOSITION XII . THEOREM . 109. If two parallel lines PARALLEL LINES . 27.### 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.