Elements of Geometry, Part 1Harper & Brothers, 1896 - Geometry |
From inside the book
Results 1-5 of 22
Page 6
... Angles with a common vertex and side , as a and b , are said to be adjacent . 15. Def . - Two angles are equal if they BOOK I FIGURES FORMED BY STRAIGHT LINES.
... Angles with a common vertex and side , as a and b , are said to be adjacent . 15. Def . - Two angles are equal if they BOOK I FIGURES FORMED BY STRAIGHT LINES.
Page 7
... adjacent angles are equal , each of these angles is a right angle , and the lines are perpen- dicular . A C RIGHT ANGLES B ACUTE ANGLE OBTUSE ANGLE Thus , if the angles AOC and COB are equal , they are right angles , and CO is ...
... adjacent angles are equal , each of these angles is a right angle , and the lines are perpen- dicular . A C RIGHT ANGLES B ACUTE ANGLE OBTUSE ANGLE Thus , if the angles AOC and COB are equal , they are right angles , and CO is ...
Page 12
... angles . b A X C a B M GIVEN - the straight line CM meeting the straight line AB at M and forming the angles a and b ... adjacent angles . 24. COR . I. If one of the angles formed 12 PLANE GEOMETRY.
... angles . b A X C a B M GIVEN - the straight line CM meeting the straight line AB at M and forming the angles a and b ... adjacent angles . 24. COR . I. If one of the angles formed 12 PLANE GEOMETRY.
Page 13
... angles formed by the intersec- tion of two straight lines is a right angle , the others are right angles . ( Fig . 1. ) Hint . - Apply Proposition III . ab dc b + ** FIG . I b FIG . 2 d e d FIG . 3 C ... adjacent angles are BOOK I 13.
... angles formed by the intersec- tion of two straight lines is a right angle , the others are right angles . ( Fig . 1. ) Hint . - Apply Proposition III . ab dc b + ** FIG . I b FIG . 2 d e d FIG . 3 C ... adjacent angles are BOOK I 13.
Page 14
... angles are together equal to two right angles , their exterior sides are in the same straight line . [ The converse ... adjacent , and their difference is one right angle , how large is each ? Question . The angles on the same side ...
... angles are together equal to two right angles , their exterior sides are in the same straight line . [ The converse ... adjacent , and their difference is one right angle , how large is each ? Question . The angles on the same side ...
Other editions - View all
Common terms and phrases
ABCD adjacent angles altitude angles are equal angles of parallel apothem assigned quantity bisecting centre chord circumference circumscribed circle coincide decagon diagonals diameter distance divided Draw equal circles equilateral triangle Exercise exterior angle figure Find the area GEOMETRY given circle given line given point given straight line GIVEN TO PROVE given triangle GIVEN-the Hence homologous sides hypotenuse included angle intersection isosceles triangle length line parallel lines are parallel locus mean proportional measured by arc middle points number of sides opposite sides parallel axiom parallel to BC parallelogram perimeter PLANE GEOMETRY Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rectangle regular inscribed regular polygon right angles right triangle segment similar polygons straight line joining tangent THEOREM third side third straight line triangle ABC triangle whose sides triangles are equal unequal vertex vertices
Popular passages
Page 248 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Page 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Page 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 47 - ... the third side of the first is greater than the third side of the second.
Page 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.
Page 140 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.