The length of a degree at the equator is 69 miles. Kinds of Angles Which one of these angles is a right angle? Why? Which is less than a right angle? Which is greater than a right angle? A right angle is an angle of 90°. An acute angle is an angle less than 90°. An obtuse angle is an angle greater than 90°. TRIANGLES A triangle is a surface bounded by three straight lines. (Tri means three.) A vertex of a triangle is a point where two sides meet. The base of a triangle is the side on which it seems to rest. The altitude of a triangle is the perpendicular distance from the vertex opposite the base to the base, or the base extended. Triangles are named in two ways: (1) Right-angled triangles. (2) Acute-angled triangles. right angle.) (One right angle.) (3) Obtuse-angled triangles. (One angle greater than a right angle.) RIGHT-ANGLED II. From their sides: ACUTE-ANGLED OBTUSE-ANGLED (1) Equilateral. (Having three sides equal.) Measuring degrees and angles. 1. How many right angles are there in the square? 2. How many right angles are there in the rectangle? 3. Cut from paper a square. Fold it on the line connecting the opposite corners, and cut it into two triangles. SCALENE SQUARE RECTANGLE 4. How many degrees are there in each angle of each triangle thus formed? 5. Every right triangle contains how many degrees? By Geometry it is shown that the sum of the angles in any triangle is equal to 180°. This can also be shown by measuring the angles with a protractor. The sum of all the angles of any triangle is equal to two right angles, or 180°. ་ The following numbers in each case represent the size of two angles of a triangle. Find the size of the third angle: A quadrilateral is a surface having four straight sides. (Quadrilateral means having four sides.) A SQUARE B RECTANGLE 1. Examine the quadrilaterals. What are the essential features of A? A square is a quadrilateral having four equal sides and four right angles. 2. What are the essential features of B? In what way does figure B differ from figure A? A rectangle is a quadrilateral having four straight sides and four right angles. 3. Show that the opposite sides of a rectangle must be equal and parallel. Is a square a rectangle? A parallelogram is a quadrilateral whose opposite sides are parallel, C D 4. Examine these quadrilaterals. Why are they parallelograms? How do the sides of surface compare in length? Show that its angles are not right angles. RHOMBUS RHOMBOID A rhombus is a quadrilateral whose sides are equal, and whose angles are not right angles. 5. Why is surface D a parallelogram ? Show that its angles are not right angles. Show that its sides are not equal. A rhomboid is a quadrilateral whose opposite sides are equal and whose angles are not right angles. 6. Why is surface E a quadrilateral? Why is it not a parallelogram? How many of its sides are parallel? E TRAPEZOID F TRAPEZIUM A trapezoid is a quadrilateral having but two sides parallel. 7. Why is surface F not a trapezoid? What is its name? A trapezium is a quadrilateral having no two sides parallel. 8. Describe each of the six quadrilaterals named above with reference to its sides and angles. How many of these quadrilaterals are parallelograms? Give reasons. AREAS OF RECTANGLES Finding the area of a rectangle. Find the area of a rectangle 4 yd. long and 3 yd. wide. How long is this rectangle? how wide? What is the unit of measure? How many such units are in the first row? in the second? in the entire surface? 4 yd. sa y 3yd. If the length and width of a rectangle are expressed in inches, the unit of measure is 1 sq. in.; if expressed in feet, the unit of measure is 1 sq. ft.; if expressed in rods, the unit of measure is 1 sq. rd. If the length and width are expressed in related units, as feet and inches, or yards, feet, etc., the dimensions must be changed to like units before finding the area, that is the number of square units it contains. Written Work 1. Find the area of a flower bed 20 feet 8 inches in length by 10 feet 6 inches in width. The area of a rectangle is found by multiplying its unit of measure by the product of its two dimensions when expressed in like units. Find the areas of rectangles having the following dimensions: 10. How many square yards are there in a lawn 45 feet long and 36 feet wide? 11. A square ball-park 600 feet on a side is inclosed with a tight board fence 9 feet in height. Find the outside surface of the fence in square yards. 12. Compare in area a surface 8 inches square and a surface 2 inches square; a surface 20 rods square and a surface 40 rods square. 13. Bricks are generally 8 in. x 4 in. x 2 in. in size. Estimate the number necessary to lay a sidewalk 100 ft. long and 5 ft. wide, if the bricks are laid on the flat side. Find the cost of the bricks needed at $13.75 per thousand. |