8.4 Constructing Angle Bisectors

When you divide an Angle into two equal parts.... you bisect the angle. There are several ways to bisect an angle: • Paper Folding • Using a mira • Use a compass. • Use a protractor. • Ask a math teacher to do it for you. • Use a triangle and a ruler. Protractor: Q. How can you use your protractor to check your work? - make sure the two angles you have created are the same - make sure the two angles add up to the measurement of the original angle Practice: Page 312 and 313....3,4,5,6,and 7 You must use your protractor to construct the angles!

8.3 - Constructing Perpendicular Bisectors

Focus......Use a variety of methods to construct perpendicular bisectors of Line segments Bisect means to cut in half. When you bisect a line....you cut it in half. If you construct the bisector at right angles (90 degrees) to the line segment.....you've constructed a Perpendicular Bisector. There are several ways to construct perpendicular bisectors: a) Use paper folding. b) Use a compass. c) Use a mira. d) Use a ruler. Method 1 - Paper Folding 1. Draw a line segment AB (about 10cm) 2. Fold the line in half so that Point B is on top of point A. 3. Draw a line down the crease in your paper. This is your perpendicular bisector. Method #2 - Mira 1. Draw a line segment AB (10cm) 2. Place the mira in the middle of the line segment, the reflection of Point A should be on top of Point B (otherwise your line won't be straight). 3. Draw a line down the mira Method #3 - Use a Compass... Method #4 - Ruler 1.) Draw a line segment AB (10 cm) 2.) Place the ruler on a diagonal so that A is on one side of the ruler and B is on the other side. 3.) Draw a line segment down each side of the ruler. 4.) Turn the ruler so that A and B are on opposite sides of the ruler and draw line segments again. 5.) Label the points where the line segments meet, Point "C" and Point "D". 6.) Connect C and D to create a new line segment. CD is perpendicular to AB. Homework: pg. 308-309 # 1-7

8.2 Perpendicular Lines

Focus: Use different methods to construct and identify perpendicular Line segments Materials: Ruler, triangle, protractor, compass, graph paper. Activity (with a partner) 1. Draw a line segment (7-8 cm long) on graph paper. 2 Using the tools provided(and your imagination), construct a second line segment perpendicular to the first. Complete 1 and 2 above in as many ways as you can. Try to find (at least) 3 different methods. Notes: 2 line segments are perpendicular if they intersect (meet) at a right angle(90 degrees) How can we construct Perpendicular Lines? 1. Use a plastic triangle. 2. Use paper folding. 3. Ruler and a protractor. 4. Use a mira. 5.Use a ruler and a compass. (see page 304) List Pairs of Lines which are Perpendicular:

Squares are also sets of perpendicular lines. Homework page 305....1 to 5

8.1 Parallel Lines

Focus - Use different methods to construct and identify parallel lines. Parallel Lines are lines on the same flat surface that never meet...they are the same distance apart, no matter where you measure. 3 different methods... 1) Ruler…Put a ruler down and draw a line on either side of the ruler. 2) Use a Compass… Make a line segment with a straight edge. Put a POINT at each end of this line segment and name these points….A and B. Put 2 points on the line about 4 cm apart. Name these 2 Points….E and F. Using your compass and a radius of 3 cm….. make 2 circles on your line segment….using points E and F as your circle centers. Strike a line from the top of 1 circle to the top of the other. Where this line contacts the circle……label the points…..H and I 3) Use a Protractor… Construct Line Segment AB. Place the protractor on the line segment. Mark 90° on the paper. Slide your Protractor 3-4 cm down the line segment and place a second point at 90°. Connect these two points with a ruler……name this new line segment MN

7.6 Tree Diagrams

Focus: investigate outcomes of probability experiments Explore: p. 284 (build a chart that will organize all your information below) List all possible combinations when you spin a five-colour spinner and flip a coin: Calculate the theoretical probability of each combination : Carry out an experiment of 100 spins/flips to determine the experimental probability of each combination you determined previously:

If you determine probability with cards, spinners, coins, dice, etc....you are performing EXPERIMENTAL PROBABILITY. If you calculate probabilities using a mathematical formula...you are performing THEORETICAL PROBABILITY. If you are calculating the probability of two separate events, where the results of one event have nothing to do with the other, the events are...INDEPENDENT EVENTS. We can use a tree diagram to show all possible outcomes for an experiment with two separate events. All the possible outcomes can be listed in what is called a SAMPLE SPACE. Eg. P(Green and Heads) - spinner and penny...

Remember the formula for probability is P(event) = # of favorable outcomes/(divided by) total # of possible outcomes So, the ratio is 1:10, the probabiltiy is 1/10. Practice - pg. 287 #1-6

7.5 Different Ways to Express Probability

Focus: express probabilities as ratios, fractions and percent As a mathematical formula, we can express probability: P(event) = # of Favourable Outcomes # of Possible Outcomes So, the Probability of an event can be calculated as the # of favorable outcomes, divided by the total # of all possible outcomes. Explore - p. 279: Complete the chart using the information in the textbook and the examples given: Probability can be expressed as a: - ratio - fraction - percent

A certain event is one that will always happen and is expressed as 1 or 100% - rolling a number on a regular six-sided die is a certain event An impossible event is one that will never occur and is expressed as 0 or 0% - rolling the number 7 on a regular six-sided die is an impossible event All probability is between 0.0 and 1.0 (the decimal form of the calculated percentage) or 0% and 100% *Complete the Example on p. 281 *Practice - Page 282-283 - #1-7

7.4 Application of Averages

Focus: understand which average best describes a set of data. Explore - page 271

Question to Ponder... Which measure best describes the average number of siblings? Mode, mean and median are all types of averages; they are called...Measures of Central Tendency the Mean is usually the best average if numbers in the data are not significantly different from one another the Median is usually the best measure if there are numbers in the data that are significantly different from one another the Mode is usually the best measure of average if the data is about measurements or sizes Eg. Shoes, Clothing, Windows Connect - page 271

The mean is 30.7 - not an actual pant size, so not very useful The median is 30 - tells us half bought bigger sizes, half bought smaller sizes The modes are 28 and 30 - tells us which sizes were bought most In this case, the mode is best as it tells us what sizes we need more of as they are most popular... Practice page 273-274, #1-3 and 6 Stem and Leaf Plot Required!!!!