Plane Geometry |
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Page 7
... show the truth of an assertion . In the course of a geometrical proof we proceed from inference to inference , and we may appeal to any or all of the follow- ing to the definition of a term previously agreed on ; to an axiom or a ...
... show the truth of an assertion . In the course of a geometrical proof we proceed from inference to inference , and we may appeal to any or all of the follow- ing to the definition of a term previously agreed on ; to an axiom or a ...
Page 15
... Show that Theorem 3 applies . 6. In a certain rectilinear four - sided figure the opposite sides are equal . Prove that a line joining two opposite vertices forms two equal triangles . HINT . Use § 33 . 7. ABCDE is a rectilinear figure ...
... Show that Theorem 3 applies . 6. In a certain rectilinear four - sided figure the opposite sides are equal . Prove that a line joining two opposite vertices forms two equal triangles . HINT . Use § 33 . 7. ABCDE is a rectilinear figure ...
Page 19
... Why , you can see that it is true . " The following illus- trations , however , will show that the eye may easily be deceived , and that an appeal to the eye is not a proof . 9. Which appears to be the longer in the adjacent BOOK I 19.
... Why , you can see that it is true . " The following illus- trations , however , will show that the eye may easily be deceived , and that an appeal to the eye is not a proof . 9. Which appears to be the longer in the adjacent BOOK I 19.
Page 30
... shows that the converse is false . Even outside of geometry the converse of a theorem is not always true . This will be apparent from stating the con- verse of the following : If a man lives in Chicago , he lives in Illinois . These ...
... shows that the converse is false . Even outside of geometry the converse of a theorem is not always true . This will be apparent from stating the con- verse of the following : If a man lives in Chicago , he lives in Illinois . These ...
Page 43
... shows to be necessary . 2. Select two triangles which appear to be congruent and which contain as parts the lines or angles to be proved equal . It will often be found necessary to draw lines not mentioned in the theorem in order to ...
... shows to be necessary . 2. Select two triangles which appear to be congruent and which contain as parts the lines or angles to be proved equal . It will often be found necessary to draw lines not mentioned in the theorem in order to ...
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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.