Plane Geometry |
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Page 27
... . But ≤1 + 22 = Z3 + Z4 . ( 2 ) 6 . ≤2 = 23 . 5. § 36. All straight angles are equal . 6. ( 2 ) - ( 1 ) , § 51. If equals are subtracted from equals , the results are equal . 58. Corollary . A corollary is a secondary , or BOOK I 27.
... . But ≤1 + 22 = Z3 + Z4 . ( 2 ) 6 . ≤2 = 23 . 5. § 36. All straight angles are equal . 6. ( 2 ) - ( 1 ) , § 51. If equals are subtracted from equals , the results are equal . 58. Corollary . A corollary is a secondary , or BOOK I 27.
Page 28
Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton. 58. Corollary . A corollary is a secondary , or a minor , theorem dependent on a major theorem . Usually it is a theorem the truth of which is apparent from the major ...
Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton. 58. Corollary . A corollary is a secondary , or a minor , theorem dependent on a major theorem . Usually it is a theorem the truth of which is apparent from the major ...
Page 29
... corollaries all necessary reasons should be given in full , whether they are given in the text or not . 60. Corollary 2. If two parallel lines are cut by a transversal , the sum of the two interior angles on the same side of the trans ...
... corollaries all necessary reasons should be given in full , whether they are given in the text or not . 60. Corollary 2. If two parallel lines are cut by a transversal , the sum of the two interior angles on the same side of the trans ...
Page 30
... corollaries in §§ 59 , 60 , and 62 respectively . It is important to note that the converse of a theorem is not always true . Thus : If a quadrilateral is a square , its diagonals intersect at right angles . Conversely : If the ...
... corollaries in §§ 59 , 60 , and 62 respectively . It is important to note that the converse of a theorem is not always true . Thus : If a quadrilateral is a square , its diagonals intersect at right angles . Conversely : If the ...
Page 32
... corollaries to Theorem 11 . A α Ков 2 6 5 C B 3 b C 4/8 D 65. Axiom V. A number may be substituted for its equal in any operation on numbers . NOTE . It should be observed that the axioms stated from time to time apply to numbers . If ...
... corollaries to Theorem 11 . A α Ков 2 6 5 C B 3 b C 4/8 D 65. Axiom V. A number may be substituted for its equal in any operation on numbers . NOTE . It should be observed that the axioms stated from time to time apply to numbers . If ...
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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.