Plane Geometry |
From inside the book
Results 1-5 of 100
Page
... exercises . The chief aim of the authors in preparing this text has been to give such assistance to students as will stimulate insight and develop power to solve exercises of gradually increasing difficulty . The content and ...
... exercises . The chief aim of the authors in preparing this text has been to give such assistance to students as will stimulate insight and develop power to solve exercises of gradually increasing difficulty . The content and ...
Page
... Exercises based on angle sums are presented on page 35 , at which point the student begins his really independent work upon numerical exercises . Having acquired some ability in solving numerical exercises he is prepared to begin the de ...
... Exercises based on angle sums are presented on page 35 , at which point the student begins his really independent work upon numerical exercises . Having acquired some ability in solving numerical exercises he is prepared to begin the de ...
Page
... Frank Charles Touton. CONTENTS THE ORIGIN OF GEOMETRY PAGE 1 Book I BOOK II . BOOK III 3 89 155 Book IV 214 Book V .. 249 SUPPLEMENTARY EXERCISES 286 PLANE GEOMETRY THE ORIGIN OF GEOMETRY The elementary geometry of vii.
... Frank Charles Touton. CONTENTS THE ORIGIN OF GEOMETRY PAGE 1 Book I BOOK II . BOOK III 3 89 155 Book IV 214 Book V .. 249 SUPPLEMENTARY EXERCISES 286 PLANE GEOMETRY THE ORIGIN OF GEOMETRY The elementary geometry of vii.
Page 13
... EXERCISES 3. State Theorem 2 , using the word isosceles . 4. If the three sides of a triangle are equal , its three angles are equal . HINTS . Prove by using Theorem 2 twice . Write down the several steps of the proof as in the proof of ...
... EXERCISES 3. State Theorem 2 , using the word isosceles . 4. If the three sides of a triangle are equal , its three angles are equal . HINTS . Prove by using Theorem 2 twice . Write down the several steps of the proof as in the proof of ...
Page 15
... EXERCISES 5. In a triangle ABC line CK is drawn from C to the middle point of AB . If AC and BC are the same length , prove that AACK is congruent to ABCK . HINT . Show that Theorem 3 applies . 6. In a certain rectilinear four - sided ...
... EXERCISES 5. In a triangle ABC line CK is drawn from C to the middle point of AB . If AC and BC are the same length , prove that AACK is congruent to ABCK . HINT . Show that Theorem 3 applies . 6. In a certain rectilinear four - sided ...
Other editions - View all
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.