![]() Use the Point Tool to create a point that is not on the line. Use the Line Tool to draw a line anywhere on the sketch. Remember that the Line Tool has two arrows do not use the Segment Tool. Problem B6 developed by Educational Development Center, Inc. Problem B5 adapted from IMPACT Mathematics, Course 1, developed by Educational Development Center, Inc. How can you change your original quadrilateral to make the inside quadrilateral a square? What changes on the inside quadrilateral? What stays the same? Move around your original quadrilateral, changing its shape. How could you test to see if you are right about the kind of quadrilateral you have in the center? What measurements could you make? Construct the midpoints of all four sides of the quadrilateral, and then connect them in order.ĭescribe the quadrilateral in the center. ![]() You may want to use the facts about corresponding angles and vertical angles, or you may come up with another explanation.Ĭreate any quadrilateral with Geometer’s Sketchpad. ![]() ∠2 +∠7 = 180° (because they are adjacent angles of a parallelogram)Īlternate interior angles (angles on opposite sides of the transversal, and between the parallel lines, like∠7 and∠3 or∠2 and∠8), also have the same measure.Ĭreate an argument to explain why the above statement about alternate interior angles would be true. ∠1 +∠2 = 180° (because they form a straight line) So, to prove that ∠1 and∠7 are congruent, we write the following: By doing so we have created a parallelogram, and thus we know that the adjacent angles of a parallelogram (in this case ∠2 and ∠7) equal 180°. To prove that corresponding angles are congruent, we could add another line segment,, parallel to line j. Now ∠1 sits exactly where ∠7 used to be, ∠3 sits exactly where ∠5 used to be, and so on. One way to understand this is to imagine sliding a copy of the picture above along line j until line k sits on top of line l. When two parallel lines both intersect a third line, corresponding angles (angles in the same relative positions, like angles 1 and 7 or angles 3 and 5 in the picture below) have the same measure. What other pair of angles is equal in measure? Why? In this problem, you will look at an explanation for why vertical angles have the same measure. When two lines intersect, the vertical angles (angles opposite each other) have the same measure. Mathematics requires a reasoned argument that is general, not about a specific set of lines. But evidence alone doesn’t explain why something is true, or even mean that it is true. In the previous subpart, you gathered evidence of some properties of angles. What else do you need to construct a line parallel to your original line?Ĭontinue your construction and record the steps you used to construct two parallel lines. This is Sketchpad’s way of telling you that you don’t have the correct objects selected or you don’t have enough objects selected. You’ll notice that the “Parallel Line” is gray - therefore, not an option to you. Pull down the Construct menu in Sketchpad. Using the Line Tool in Geometer’s Sketchpad, draw a line. Note 2įollow these steps to construct two parallel lines: a. With dynamic geometry software, you can draw two lines that look parallel, but you can’t be sure that they are parallel unless you construct them to be parallel. Another way to think about parallel lines is that they are “everywhere equidistant.” No matter where you measure, the perpendicular distance between two parallel lines is constant. Parallel lines are two lines in the same plane that never intersect.
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