# Elementary Geometry: Practical and Theoretical

University Press, 1903 - Geometry - 355 pages

### Contents

 Angles of a triangle 76 Angles of a polygon 83 Congruent triangles 85 Constructions 103 Construction of triangles from given data 113 Inequalities 119 Parallelograms 132 Subdivision of a straight line 141 Intersection of loci 148 Miscellaneous Exercises 154 Area of parallelogram 167
 Area of Circle 284 288 288 SIMILARITY 301 64 302 Similar Triangles 313 Rectangle Properties etc 326 Similar Polygons 337 70 342 Miscellaneous Exercises 345 List of Definitions 352 80 354

### Popular passages

Page 88 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 269 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 206 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 342 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 270 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 186 - This sub-division shows that the square on the hypotenuse of the above right-angled triangle is equal to the sum of the squares on the sides containing the right angle.
Page 206 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 136 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Page 214 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 123 - The difference between any two sides of a triangle is less than the third side.