Directions: Working with your group, cut out the shapes below and sort them into 3 groups based on similar characteristics.
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- Dwight Mathews
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1 Directions: Working with your group, cut out the shapes below and sort them into 3 groups based on similar characteristics.
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3 1) In the space below, explain how you grouped your triangles. Label your groups: 1, 2 and 3. Label the triangles in group 1: 1a, 1b, and 1c. Label the triangles in group 2: 2a, 2b, and 2c. Label triangles in group 3: 3a,3b, and 3c. Now, pick up the triangles in group 1. Match up the corresponding angles by placing one triangle on top of the other, lining up the corners. Do this for each pair of corresponding angles. Then do the same thing for the triangles in group 2 and then in group 3. 2) What do you notice about the angles in similar figures? Now you will be measuring the angles using a protractor (on your Geometer). Pick up triangles 1c, 2c, and 3c only. Measure all three angles in triangles 1c, 2c, and 3c, labeling the angles appropriately. Next, label the angles of all the remaining triangles using the rule you discovered in question 2. DO NOT USE THE PROTRACTOR! Pick up the triangles in group 3. Label the sides that are corresponding. Now, pick up triangles 3a and 3b and measure the lengths of each side in inches. Record your measurements in the table below. Triangle 3a Triangle 3b Ratio of side b to side a
4 Now pick up triangles 3b and 3c and measure the lengths of each side in inches. Record your measurements in the table below. Triangle 3b Triangle 3c Ratio of side b to side c Now pick up triangles 3a and 3c and measure the lengths of each side in inches. Record your measurements in the table below. Triangle 3a Triangle 3c Ratio of side c to side a Now pick up the triangles in group 2. Measure the sides of triangle 2a only and label the triangle with the measurements. Measure only ONE side of 2b and only ONE side of 2c. Label these sides and set the ruler aside. Use what you know about the sides of 2a to help you determine the lengths other two sides of 2b and the other two sides of 2c. DO NOT USE A RULER FOR MORE THAN ONE side of each remaining triangle. What did you notice as you determined the lengths of the remaining sides? How were you able to find the missing lengths?
5 Now pick up the triangles in group 1. Measure the sides of triangle 1c only and label the triangle with the measurements. Measure only ONE side of 1a and only ONE side of 1b. Label these sides and set the ruler aside. Use what you know about the sides of 1c to help you determine the lengths other two sides of 1a and the other two sides of 1b. DO NOT USE A RULER FOR MORE THAN ONE side of each remaining triangle. What did you notice as you determined the lengths of the remaining sides? How were you able to find the missing lengths? Drawing Conclusions: 1) Write definitions of the following vocabulary terms in your own words: a) similar figures b) corresponding angles c) corresponding sides d) scale factor 2) List three things you learned about similar figures:
6 3) The following figures are similar. Fill in the lengths of the sides for the second figure if the scale factor is ft 3 ft 3 ft 2 ft 4) The following figures are similar. If A = 95, B = 85, C = 90, and D = 90, find W, X, Y, and Z. A B W X D C Z Y List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons. 5. ABDF VXZT 6. DFG KMJ Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning
7 Each pair of polygons is similar. Find the value of x
8 15. Rectangle ABCD has a width of 8 yards and a length of 20 yards. Rectangle QRST, which is similar to rectangle ABCD, has a length of 40 yards. Find the scale factor of rectangle ABCD to rectangle QRST and the perimeter of each rectangle. Find the perimeter of the given triangle. 16. DEF, if ABC DEF, AB = 5, BC = 6, AC = 7, and and DE = WZX, if WZX SRT, ST = 6, WX = 5, and the perimeter of SRT = 15
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