Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 35
... line can be drawn through A parallel to BC , for , by Axiom II . , it would have the same direction as AE , and ... secant line and not adjacent - as 1 , 3 - or 2 , 4 - are called alternate - exterior angles . Two interior angles on ...
... line can be drawn through A parallel to BC , for , by Axiom II . , it would have the same direction as AE , and ... secant line and not adjacent - as 1 , 3 - or 2 , 4 - are called alternate - exterior angles . Two interior angles on ...
Page 36
... line AB cut the lines CD and EF , making the alternate - interior angles CAB and ABF equal ; then are CD and EF ... secant line is equal to two right angles , the two lines are parallel . Suggestion . Show that a pair of alternate ...
... line AB cut the lines CD and EF , making the alternate - interior angles CAB and ABF equal ; then are CD and EF ... secant line is equal to two right angles , the two lines are parallel . Suggestion . Show that a pair of alternate ...
Page 37
... line , the alternate - interior angles are equal . Let the parallel lines CD and EF be cut by the line AB ; then ... secant line is equal to two right angles . EXERCISE . Theorem . - A line perpendicular to one of two parallel lines is ...
... line , the alternate - interior angles are equal . Let the parallel lines CD and EF be cut by the line AB ; then ... secant line is equal to two right angles . EXERCISE . Theorem . - A line perpendicular to one of two parallel lines is ...
Page 54
... lines are cut by a third , if a pair of corresponding angles are equal , the lines are parallel . Corollary II . When two straight lines are cut by a third , if the sum of two interior angles on the same side of the secant line is equal ...
... lines are cut by a third , if a pair of corresponding angles are equal , the lines are parallel . Corollary II . When two straight lines are cut by a third , if the sum of two interior angles on the same side of the secant line is equal ...
Page 62
... line AB at the point C. A secant is a straight line which E meets the circumference in two points ; as EF . A B Two circumferences are tangent to each other when they are both tangent to the same straight line at the same point . 21 ...
... line AB at the point C. A secant is a straight line which E meets the circumference in two points ; as EF . A B Two circumferences are tangent to each other when they are both tangent to the same straight line at the same point . 21 ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - 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 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.