Plane Geometry |
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Page 178
... compute by any other method . The example cited indicates the value of what is called the graphical method of ... computation to the eye so that its various relations can be readily grasped . Its greatest advantage for certain classes of ...
... compute by any other method . The example cited indicates the value of what is called the graphical method of ... computation to the eye so that its various relations can be readily grasped . Its greatest advantage for certain classes of ...
Page 185
... compute the other angle and the other sides . * . In Exs . 98-102 , inclusive , give answers in simplest algebraic form , merely indicating the roots involved , EXERCISES 94. If the acute angles of a right triangle BOOK III 185.
... compute the other angle and the other sides . * . In Exs . 98-102 , inclusive , give answers in simplest algebraic form , merely indicating the roots involved , EXERCISES 94. If the acute angles of a right triangle BOOK III 185.
Page 189
... compute approximate values for the ratios of 20 ° . Compare the results obtained with those given in the table . 108 ... computed by means of the trigonometric ratios . Example . In the triangle ABC the angle A is 24 ° and AC is 42. Find ...
... compute approximate values for the ratios of 20 ° . Compare the results obtained with those given in the table . 108 ... computed by means of the trigonometric ratios . Example . In the triangle ABC the angle A is 24 ° and AC is 42. Find ...
Page 205
... compute the height of the pole ? 167. Is a triangle whose sides are 3 , 4 , and 5 respectively or any multiple of these numbers a right triangle ? Prove . 168. How can a tape line and the fact . just proved be used to locate stake D so ...
... compute the height of the pole ? 167. Is a triangle whose sides are 3 , 4 , and 5 respectively or any multiple of these numbers a right triangle ? Prove . 168. How can a tape line and the fact . just proved be used to locate stake D so ...
Page 206
... compute AB . B K R 171. In the right - hand figure above , the points A and B are accessible , but the line AB cannot be directly measured . What lines can be laid out and measured that will enable one to compute AB ? ` Assume values ...
... compute AB . B K R 171. In the right - hand figure above , the points A and B are accessible , but the line AB cannot be directly measured . What lines can be laid out and measured that will enable one to compute AB ? ` Assume values ...
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Common terms and phrases
AABC acute angle adjacent angles adjacent figure algebra altitude angles are equal apothem arc BC Axiom base bisector bisects central angle chord circumference circumscribed common tangent compute congruent Construct a triangle Converse of Theorem convex polygon Corollary cuts decagon diagonals diameter divided Draw drawn equal angles equal circles equal respectively equiangular equilateral triangle equivalent EXERCISES exterior angle Find the area Find the number geometry Given the triangle greater hexagon HINT hypotenuse hypothesis inches inscribed angle intersect isosceles triangle length line-segment locus measured median mid-perpendicular mid-point number of degrees number of sides parallelogram perimeter perpendicular plane Proof proportional prove quadrilateral QUERY radii radius ratio rectangle regular inscribed regular polygon rhombus right angles right triangle secant segments square straight angle straight line tangent third side trapezoid triangle ABC vertex vertices
Popular passages
Page 224 - ... 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 182 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle...
Page 80 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first 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 26 - The two pairs of angles 3 and 6, 4 and 5, are called alternate interior angles ; and the two pairs of angles if 1 and 8, 2 and 7, are called alternate exterior angles. The four pairs of angles 1 and 5, 2 and 6, 3 and 7, and 4 and 8 are called corresponding angles.
Page 69 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 230 - 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, minus twice the product of one of these sides and the projection of the other side upon it.
Page 184 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 175 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 192 - If two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other.
Page 242 - Prove that the area of the square on the hypotenuse of a right triangle equals the sum of the areas of the squares on the other two sides.