Lessons in Geometry: For the Use of Beginners |
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Common terms and phrases
ABCD Fig adjacent angles altitude angle BAC angles are equal apothem base bisect breadth called centre chord circumference coincide cone Construct a parallelogram Construct a square cube cubic curved cylinder Define Describe a circle diagonals diameter dihedral angle dimensions distance divided Draw a line Draw a plan Draw freehand drawing to scale edges equal angles equiangular equidistant equilateral triangle exercises in Lessons Find the area Find the value frustum given point height horizontal plane hypotenuse HYPOTHESIS inches inscribed inscribed angle intersection isosceles triangle italicized exercises Join Measure meter middle point miles parallelogram perimeter perpendicular prism PROOF protractor Prove pyramid radii radius ratio regular polygon Review the italicized rhombus right angle right triangle ruler and compasses similar triangles slant height straight angle straight line tangent Theorem trapezium trapezoid triangle ABC units of length vertex vertical line
Popular passages
Page 145 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 113 - These units are related as shown in the following table : 144 sq. in. = 1 sq. ft. 9 sq. ft. = 1 sq. yd. 43,560 sq. ft.
Page 90 - In this exercise, besides ruler and compasses, the scale must be used. 20. Construct a square, and on the four sides construct equilateral triangles ; join their vertices, and show by measurement that the figure so formed is also a square. Can you prove that it is a square ? Lesson 46. 1. Define an equilateral polygon. An equilateral polygon is a polygon whose sides are equal. 2. Define an equiangular polygon. An equiangular polygon is a polygon whose angles are equal. 3. Define a regular polygon....
Page 66 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 133 - What will it cost, at $2 per rod, to fence a square field containing 2£ acres? 3. How many five-acre lots can be made out of a field containing 5 square miles? 4. How many planks, each 10 ft. long and 8 in. wide, will cover a floor 14 ft. 3 in. long and 13 ft. 4 in. wide? 5. Find the side of a square having an area equal to that of a regular hexagon whose side is 8 ft. 6. The circumferences of two concentric circles are 440 ft. and 330 ft., respectively. Find the width of the ring. 7. Out of a circular...
Page 73 - Every point in the bisector of an angle is equidistant from the sides of the angle. Hyp. Z DAB = Z DAC and 0 is any point in AD. To prove 0 is equidistant from AB and AC. Draw OP _L AB and OP' _L AC, and prove the equality of the two triangles.
Page 163 - The distance around a reservoir in the shape of a regular hexagon is 360 ft. If the average daily loss from evaporation amounts to a layer of water 2 in. deep, how many cubic feet of water must be supplied daily to maintain the water at a constant level?
Page 172 - FIG. 171. 3. How is the surface of a sphere found ? It can be proved that the surface of a sphere is equal to the, lateral surface of the circumscribed cylinder. Let r denote the radius of a sphere. Then r is also equal to the radius of the base of the circumscribed cylinder, and 2 r is its height ; therefore its lateral surface is equal to 2irr x 2r, or 4 TIT* (p.
Page 113 - CHAPTER VII. AREAS. Lesson 6O. 1. How are surfaces measured? Surfaces, like lines, are measured by choosing a unit, and then finding how many times this unit is contained in the surface which we wish to measure. The number of times the unit is contained in the surface to be measured, followed by the name of the unit, is called the area of the surface. 2. What units of area are in common use ? The square inch, the square foot, the square yard, the acre, and the square mile. All these units, except...
Page 40 - Lesson 19. 1. Define perpendicular lines and oblique lines. If two lines form a right angle, they are said to be perpendicular to each other ; if they form any other angle, they are said to be oblique to each other. Abbreviation : The sign _L means " perpendicular." 2. Problem. — To erect a perpendicular at any point C of a given straight line AB. METHOD I. (Fig. 40) . — Instruments : ruler and compasses. With centre (7, and any radius, cut AB in D and E. With centres D and .E, and a greater...