Learning Resources

Lesson

To do the investigation on the slopes of parallel and perpendicular lines you can follow the steps for Investigation 3 on page 222 in your text or you can use the Geometer's Sketch Pad interactive window provided in this lesson. Regardless of the method you use, you will need the following materials to work on this lesson and the assigned activities:

1. graph paper
2. a ruler

Text method

If you use this method, open your text to page 222 now and proceed. The instructions are fairly straightforward. If you prefer, you can get in groups of two or three to complete this investigation. If you do have difficulty, you can go here for some help and hints.

GSP Interactive method

The first interactive window investigates the relationship between the slopes of parallel lines. For instructions go here.

The second interactive window investigates the relationship between the slopes of perpendicular lines. For instructions go here.

Whichever method you use, make sure you answer Step C of Investigation 3 before continuing.

The key ideas in this lesson are contained in Step C of the investigation. If you have done it properly you should have arrived at the following conclusion:

1. The slopes of parallel lines are equal.
2. The product of the slopes of perpendicular lines is  -1.  Alternately you could say that the slopes of perpendicular lines are negative reciprocals of each other ( for example: ½ and -2,  -¼ and 4, are negative reciprocals of each other). 

Although not clearly stated in the investigation, the converses of the above statements are also true, viz.

1. If the slopes of two lines are equal, then they are parallel.
2. If the product of the slopes of two lines is -1 (i.e. they are negative reciprocals of each other), then they are perpendicular.

To complete the assigned activities you will also have to use the formula, which you learned in a previous course, for calculating the slopes of lines. It states that given the points A(x₁ , y₁) and B(x₂ , y₂) , the slope formula is:

                                           

Activity

1. Complete the Investigation Questions 1 - 3 on pages 122 & 123.
2. Do the CYU Questions 4, 5, 8, 9 on page 223.

When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.

Test Yourself

1. Prove that CDFE is a trapezoid (has only one pair of opposite sides parallel), given C(-8 , 4), D(4 , 10), F(5 , 3), E(-5 , -2).  Are any of its angles right angles?

[Solution]