Elementary Geometry: Plane |
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Page 11
Plane James McMahon. Comparison of line - segments . 2. Two given line - segments may be ... given segments . It is also called the excess of the greater over the less ... ANGLES 5. An angle is the figure formed LINE - SEGMENTS AND ANGLES 11.
Plane James McMahon. Comparison of line - segments . 2. Two given line - segments may be ... given segments . It is also called the excess of the greater over the less ... ANGLES 5. An angle is the figure formed LINE - SEGMENTS AND ANGLES 11.
Page 13
Plane James McMahon. line , are called adjacent angles , and the whole angle ... given angles are then said to be added or summed . It may be stated as the ... angles . 11. Two angles are compared in LINE - SEGMENTS AND ANGLES 13.
Plane James McMahon. line , are called adjacent angles , and the whole angle ... given angles are then said to be added or summed . It may be stated as the ... angles . 11. Two angles are compared in LINE - SEGMENTS AND ANGLES 13.
Page 14
... angles are equal . If these sides do not coincide , one of the given angles is equal to the sum of the other given angle and a third angle . The first given angle is then said to be greater than the other , and the latter is said to be ...
... angles are equal . If these sides do not coincide , one of the given angles is equal to the sum of the other given angle and a third angle . The first given angle is then said to be greater than the other , and the latter is said to be ...
Page 15
... angle turned through is called a perigon . Α ' A 17. The half of a straight angle is called a right angle . B Ä A 18 ... given and illustrated ( 1-21 ) form the basis of the statements in the next section . ther definitions will be introduced ...
... angle turned through is called a perigon . Α ' A 17. The half of a straight angle is called a right angle . B Ä A 18 ... given and illustrated ( 1-21 ) form the basis of the statements in the next section . ther definitions will be introduced ...
Page 32
... given angle AOB . To prove this , draw MC and NC . The triangles OMC and ONC have their sides respectively equal ; therefore the angles MOC and NOC are equal ( 66 ) . Ex . 1 . A given angle has only one bisector . Ex . 2 . Bisect a given ...
... given angle AOB . To prove this , draw MC and NC . The triangles OMC and ONC have their sides respectively equal ; therefore the angles MOC and NOC are equal ( 66 ) . Ex . 1 . A given angle has only one bisector . Ex . 2 . Bisect a given ...
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Common terms and phrases
ABCD adjacent sides altitude angle AOB angle equal angles are equal antecedents apothem base bisector bisects called central angle central line chord circumscribed circles coincide contraposite corresponding sides Definition diagonal difference divided Draw drawn equal angles equal circles equal ratios equiangular equilateral polygon equivalent figure geometry given angle given circle given line given point given polygon given ratio greater half Hence hypotenuse hypothesis inscribed interior angles intersect isosceles triangle less Let ABC line joining line-segments magnitudes measure-number mid-point mth multiple n-gon number of sides number-correspondent opposite sides parallel parallelogram perigon perimeter perpendicular PROBLEM prolonged prove quadrangle radii radius ratio compounded ratio of similitude regular polygons respectively equal rhombus right angle right triangle segments Show similar polygons similar triangles similarly solution statement straight angle straight line subtended superposable surface symmetric tangent THEOREM triangle ABC unequal vertex vertical angle
Popular passages
Page 148 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 147 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Page 7 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 136 - If a straight line be divided into any two parts, the square on the whole line is...
Page 195 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Page 80 - 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 305 - 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 287 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 263 - If four magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals, viz.
Page 32 - At a given point in a given straight line, to construct an angle equal to a given angle. Let A be the given point in the straight line AB, and O the given angle.