Chapter Six

GeometryPrepared by: Richard Mitchell Humber College

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1Click on the computer image at the bottom right for a direct web link to an interesting Wikipedia Math Site.

CASE STUDY

6.1-Straight Lines and Angles36.1-DEFINITIONS-Pages 152 to 154

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6.1-EXAMPLE 1-Page 153Find the measure (in degrees) of angles A and B in the structureshown in Fig. 6-7.

Angle A is opposite the 340 angle and Angle B is supplementary to Angle A.

6.1-EXAMPLE 3-Page 154A portion of a street map is shown in Fig. 6-11. Find thedistances PQ and QR.

6.2 - triangles76.2-DEFINITIONS-Pages 155 to 159

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6.2-EXAMPLE 4-Page 156Find angle in Fig. 6-21.

6.2-EXAMPLE 5-Page 156Find the area of the triangle in Fig. 6-23 if the base is 52.0 and the altitude is 48.0.

52.048.0

6.2-EXAMPLE 6-Page 157Find the area of the triangle having sides of lengths 3.25, 2.16 and 5.09.

5.093.252.16

6.2-EXAMPLE 8-Page 158Two beams, AB and CD, in the framework of Fig. 6-27 areparallel. Find distance AE.

6.2-EXAMPLE 9-Page 158A right triangle has legs of length 6 units and 11 units. Find the length of the hypotenuse (c) to 3 significant digits.

= 11= 6 = ?

6.2-DEFINITIONS-Page 159Special Triangles

30o: 60o: 90o - Right Triangle45o - Right Triangle3:4:5 - Right Triangle

The side opposite the 30o angle is half the length of the hypotenuse.The hypotenuse is 2 times the length of either side.The sides are in the ratio of 3:4:5

6.3 - quadrilaterals156.3-DEFINITIONS-Page 162Quadrilaterals

Opposite sides are parallel and equal. Opposite angles are equal and each diagonal cuts the other diagonal into two equal parts.Same as parallelogram but its diagonals bisect each other at right angles and bisect the angles of the rhombus.Two sides (bases) are parallel and the altitude is the distance between the bases.

6.3-EXAMPLE 12-Page 162A solar collector array consists of six rectangular panels, each 115 cm x 235 cm, each with a blocked rectangular area (needed for connections) measuring 12.0 cm x 22.5 cm. Find the totalcollecting area in square metres.

6.4 the circle186.4-DEFINITIONS-Page 163 to 165Circles

6.4-EXAMPLE 15-Page 165Find the distance OP in Fig. 6-50.

225 cm

115 cm

6.4-EXAMPLE 16-Page 165Find the distance x in Fig. 6-52 to 3 SDs.

Diameter = 250

6.5-Volumes and Areas of Solids226.5-DEFINITIONS-Page 167Formulas for Areas and Volumes

Volume is a measure of the space it occupies or encloses (m3, cm3, ft3 etc).SURFACE AREA: Total area of the surface of a solid, including the ends or bases.

LATERAL AREA: Does not include the area of the ends or bases.CROSS-SECTIONAL AREA: Area of the plane figure obtained when we slice the solid in a specified way.6.5-EXAMPLE 17-Page 168Find the volume of a cone having a base area of 125 cm2 and an altitude of 11.2 cm.

6.5-EXAMPLE extraFind the Volume and Radius of a sphere having a Surface Areaof 462 cm2.

Step OneStep Two

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