A School Geometry, Parts 1-4Macmillan and Company, 1908 |
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Page ix
... equal to two right angles . PAGE 1 10 COR . 1. If two straight lines cut one another , the four angles so formed are together equal to four right angles . COR . 2. When any number of straight lines meet at a point , the sum of the ...
... equal to two right angles . PAGE 1 10 COR . 1. If two straight lines cut one another , the four angles so formed are together equal to four right angles . COR . 2. When any number of straight lines meet at a point , the sum of the ...
Page x
... equal . COR . 1. If the equal sides of an isosceles triangle are pro- duced , the exterior angles at the base are equal . COR . 2. If a triangle is equilateral , it is also equiangular . THEOREM 6. [ Euc . I. 6. ] If two angles of a ...
... equal . COR . 1. If the equal sides of an isosceles triangle are pro- duced , the exterior angles at the base are equal . COR . 2. If a triangle is equilateral , it is also equiangular . THEOREM 6. [ Euc . I. 6. ] If two angles of a ...
Page xi
Henry Sinclair Hall. equal , or ( ii ) an exterior angle equal to the interior opposite angle on the same side of the cutting line , or ( iii ) the interior angles on the same side equal to two right angles ; then in each case the two ...
Henry Sinclair Hall. equal , or ( ii ) an exterior angle equal to the interior opposite angle on the same side of the cutting line , or ( iii ) the interior angles on the same side equal to two right angles ; then in each case the two ...
Page xii
... equal to one another , and each diagonal bisects the parallelogram . 58 COR . 1. If one angle of a parallelogram is a right angle , all its angles are right angles . 59 COR . 2. All the sides of a square are equal ; and all its angles ...
... equal to one another , and each diagonal bisects the parallelogram . 58 COR . 1. If one angle of a parallelogram is a right angle , all its angles are right angles . 59 COR . 2. All the sides of a square are equal ; and all its angles ...
Page xiii
... equal to one another . PROBLEM 15. To find the locus of a point P which moves so that its perpendicular distances from two given straight lines AB , CD are equal to one another . INTERSECTION OF LOCI THE CONCURRENCE OF STRAIGHT LINES IN ...
... equal to one another . PROBLEM 15. To find the locus of a point P which moves so that its perpendicular distances from two given straight lines AB , CD are equal to one another . INTERSECTION OF LOCI THE CONCURRENCE OF STRAIGHT LINES IN ...
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Common terms and phrases
AB² adjacent angles altitude angle equal base BC bisector bisects circle of radius circle whose centre circles which touch circum-circle circumference circumscribed coincide common tangents concyclic Construct a triangle diagonals diagram diameter distance divided draw a circle equal in area equidistant escribed circles Euclid exterior angles Find the area find the locus given angle given circle given point given straight line given triangle greater Hence hypotenuse inches inscribed isosceles triangle length Let ABC meet metres middle point millimetre nine-points circle opposite sides orthocentre par¹ parallelogram pedal triangle perp PROBLEM produced Proof radii rect rectangle rectangle contained rectilineal figure required to prove respectively rhombus right angles right-angled triangle segment shew shewn straight line drawn tangent Theor Theorem trapezium triangle ABC triangles are equal vertex vertical angle
Popular passages
Page xi - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Page 44 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 12 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 122 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page x - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 65 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.