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Exploring Congruent Triangles Remember: The shift key will help you select more than one object at a time. Read each step fully and carefully. Many questions you may have could be answered if you fully read the question. All questions are to be answered in a Word document, printed, then turned in. Save your work in both GSP and Word often. 1) Open a Word document. Type your name date and hour in the upper right hand corner. 2) Open GSP. 3) Construct a line. (Do not construct a segment or ray.) Use the line function on the left-hand side of the frame. 4) Construct a point not on the line. 5) Select both the line and the point, and construct a perpendicular line. (Construct menu) 6) Select both lines. Construct a point at the intersection. (Construct menu) 7) Select three non-collinear points that are on the two perpendicular lines. One of the points needs to be the point of intersection of the two lines. Construct segments between these points. (Construct menu) 8) Select the original two lines and any points that are not vertices of the triangle. Hide them so that the only object on your screen is a triangle with three vertices and three segments connecting the vertices. (Display menu) Q1) What type of triangle do you have? Why? [Remember to answer all questions in Word.] 9) Label all points (use A, B, and C to label). The angle that was formed by the two perpendicular lines should be called Ð C. To do this, use the hand pointer with the letter A on it. Double-click to change a label name.10) Measure all angles by selecting 3 points in the order you would label each angle, then go to the Measure menu and select angle. (Measure menu) 11) Find the sum of the interior angles of a triangle by following these steps. § Go to the Measure menu. § Go to the Calculate function. § Your angle measures may now be selected from the value selection to use in your calculation of the interior angle measures. 12) Measure all three sides by selecting the two endpoints of a segment and measuring the distance. (Measure menu) 13) Move your triangle around. Watch the measurements change. 14) Copy and paste all of your measurements and triangle into your Word document. § In Word, shrink your picture box so that it fits within the margins. § Right click on the GSP picture to change the "wrapping" to none. § Move the picture with so that it is not covering any text. Make sure that the picture does not hide text. Q2) What is the sum of the three angle measures? Q3)
Since you have a special triangle (see question 1), what do you call side Q4) What are the other two sides called ? 15) Drag 16) Copy and paste your new triangle and your new measurements into your Word document. Q5) Are the two triangles congruent? Explain. 17) Manipulate your figure in order to find answers for question 6. Q6) Invent your own postulates or theorems! Make at least 2 conjectures or guesses of ways to prove congruent triangles using any type of triangle that you can create. Do not use SSS, SAS, or ASA - we know these work!
18) Save both your Word document ( congtri.doc) and GSP document (triangles.gsp) to a 3½" disk.19) Print your Word document. |
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