Plane Geometry |
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... proof . This is in accord with a widespread feeling that the method of limits is un- profitable for the majority of American students when they first study the plane geometry . The plan also avoids the common error of designating as a proof ...
... proof . This is in accord with a widespread feeling that the method of limits is un- profitable for the majority of American students when they first study the plane geometry . The plan also avoids the common error of designating as a proof ...
Page 7
... proof . Axioms are truths so simple that we either cannot prove them or do not care to do so . An example of a mathematical axiom is : If the same number be added to each member of an equation , the result is an equation . 18. Postulate ...
... proof . Axioms are truths so simple that we either cannot prove them or do not care to do so . An example of a mathematical axiom is : If the same number be added to each member of an equation , the result is an equation . 18. Postulate ...
Page 10
... Proof 5. AABC is congruent to AFGH . 5. § 24. The boundaries of the 26. Corresponding parts . If two triangles have the three angles of one equal respectively to the three angles of the other , any two equal angles ( one chosen from ...
... Proof 5. AABC is congruent to AFGH . 5. § 24. The boundaries of the 26. Corresponding parts . If two triangles have the three angles of one equal respectively to the three angles of the other , any two equal angles ( one chosen from ...
Page 13
... proof as in the proof of Theorems 1 and 2 above . 31. Axiom I. If equals are added to equals , the results are equal . 32. Axiom II . ( 1 ) Two numbers or magnitudes each equal to a third are equal to each other . This axiom is often ...
... proof as in the proof of Theorems 1 and 2 above . 31. Axiom I. If equals are added to equals , the results are equal . 32. Axiom II . ( 1 ) Two numbers or magnitudes each equal to a third are equal to each other . This axiom is often ...
Page 15
... proof of Theorem 3 depend on Theorem 2 ? on Theorem 1 ? If the proof of a theorem depends on Theorem 2 , does it depend on Theorem 1 ? QUERY 2. If three angles of one triangle are equal respectively to three angles of another , are the ...
... proof of Theorem 3 depend on Theorem 2 ? on Theorem 1 ? If the proof of a theorem depends on Theorem 2 , does it depend on Theorem 1 ? QUERY 2. If three angles of one triangle are equal respectively to three angles of another , are the ...
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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.