4.7 Keystroke Help
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4.7 Problem Solving Help
Help for Exercises 65 and 66 on page 248
In the graphs for Exercises 65 and 66, the figure shown is a parallelogram if both pairs of opposite sides are parallel, according to the information you are given. You know that two lines are parallel if they have the same slope, so you need to find the slopes of the opposite sides of the figure to see whether they are parallel or not. If both pairs of opposite sides are parallel, then the figure is a parallelogram.
Recall that in Lesson 4.5 you learned how to find the slope of a line using the coordinates of any two points on the line. Refer to pages 229232 if you need help remembering how to do this.
You can use the coordinates of points A, B, C, and D to find the slopes of the lines that include the sides of the figures. For example, in Exercise 65, use coordinates B(0, 4) and C(6, 7) to find the slope of the line that includes side BC. Keep in mind that both pairs of opposite sides must be parallel for the figure to be a parallelogram. If you determine that the first pair of opposite sides is not parallel, there is no need to check the remaining pair since the quadrilateral cannot be a parallelogram. If you check one pair of opposite sides and find that they are parallel, check the other pair of sides.
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