SSS SAS ASA. Supplies: Drinking straws, protractors, rulers, plain copy paper, and 3 poster papers (or electronic charts) to record class data.

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1 Teacher Notes SSS SAS ASA Supplies: Drinking straws, protractors, rulers, plain copy paper, and 3 poster papers (or electronic charts) to record class data. Teacher Set up: 1) Break class into groups of 2 students. 2) Print enough copies of this lesson so that there is one copy for each pair of students. 3) Recreate blank data tables from each of the three activities onto poster paper. There should be one poster for each activity. 4) Provide each pair of students with a copy of the lesson, 4 straws, 2 protractors, 2 rulers, and plain copy paper. Activity #1: (SSS) 2) Each student will build a triangle with their pieces of straw and measure each angle in their triangle. They may transfer straw lengths to paper, tape straws to paper, one student could hold the straws while the other student measures, etc. 3) As the groups finish the first activity, have them record their data (angle measures and side lengths) in the data table on the corresponding poster. 4) Looking at the class data as a whole, ask students to compare and contrast information from the chart. Can they draw any conclusions about triangle congruence? SSS Activity #2: (SAS) 2) Each partner will choose any two pieces of straw for sides and agree upon on one acute angle measure. Each student will use their sides and a protractor to build a triangle using the agreed upon angle measure. They will find the length of the third side and the measure of the other two angles. They may transfer straw lengths to paper, tape straws to paper, one student could hold the straws while the other student measures, etc. 3) As the groups finish the second activity, have them record their found measurements in the data table on the corresponding poster. 4) Looking at the class data as a whole, ask students to compare and contrast information from the chart. Can they draw any conclusions about triangle congruence? SAS

2 Activity #3: (ASA) 2) Each group will choose one straw length and agree upon any two acute angle measurements. They will use their one straw piece, protractor, and angle measures to form a triangle. 3) As the groups finish the third activity, have them record their found measurements in the data table on the corresponding poster. 4) Looking at the class data as a whole, ask students to compare and contrast information from the chart. Can they draw any conclusions about triangle congruence? ASA Wrap-Up: 1) As a class, summarize your findings for the day. 2) Have students complete the conclusions table at the end of this lesson by defining SSS, SAS, and ASA. 3) Have students illustrate SSS, SAS, and ASA. WARNING: Make sure that students are rounding to the nearest ¼ of an inch when measuring the sides of a triangle. Since the origonal straw lengths are a standard size, the possibilities for triangle side lengths are limited. Some measures can be very close. For example, a triangle could have sides of 3, 7, and 6.8. Students may round 6.8 to 7 and make the wrong assumption that this is an iscoselece triangle with sides lengths of 3, 7, and 7. This may cause some confusion because it is impossible to have an iscoselese triangle with 3 different angle measures. Rather, they would list their measures as 3, 7, and 6 ¾ - a scalene triangle. This may serve as a great teachable moment.

3 You and a partner need two straws per person. Have Partner A cut one of their straws to a length shorter than its original 10 inches. Discard the excess piece. Then have Partner A cut their second straw into two pieces of any length. Partner A should now have 3 straw lengths to work with. 1 st Straw 1 st Straw 2 nd Straw 2 nd Straw Before Cuts After Cuts Have Partner B cut their two straws so that they are identical to Partner A. Each partner should have identical sets to work with. We are now ready to begin. Partner A Partner B 1 st Straw 2 nd Straw 1) Have each partner create a triangle using their pieces. 2) Measure the three straw lengths and the three angles. 3) Record your data on the class chart. (To help with measuring you may tape your straws to your paper, one partner could hold the straws while other student measures, you may trace your triangle, etc.) Roster Length of Sides Angle Measures from Least to Greatest from Least to Greatest (inches) Partner A inches 37 o - 53 o - 90 o Partner B inches 37 o - 53 o - 90 o Activity#1 Summary of classroom discussion:

4 With your partner, decide on two straw pieces and agree upon on one acute angle measure. Using the straw pieces and a protractor, have each partner create the decided angle measure. Draw a dashed line connecting the two straws to form a triangle. 1) Measure the new side length and the two new angles. 2) Record your answers on the class chart. 3) Choose two different sides and a different acute angle. Build two new triangles with the new sides and new agreed upon acute angle measure. 4) Record your second set of measurements on the class chart. Roster Agreed upon Side, Angle, & Side Remaining Angles (to the nearest degree) Remaining Side (to the nearest ¼ of an inch) Partner A 3in, 75, 7 in 25, 80 6 ¾ in Partner B 3in, 75, 7 in 25, 80 6 ¾ in Activity #2 Summary of classroom discussion:

5 With your partner, choose one straw length and agree upon any two acute angle measurements, so you will be able to form a triangle to fit on paper. Using the straw piece and protractor, draw each of the acute angles to create a triangle. Each of you should build a triangle with the one straw length and the two agreed upon angles. 50 o 35 o 1) Find the measure of the missing sides and remaining angle of your triangle. 2) Record your data on the class chart. 3) Pick a new straw length and two new acute angles. Build another set of triangles. Find the measure the new sides and angle. 4) Record data in class chart. Roster Agreed upon Acute Angle, Side, & 2 nd Acute Angle New Angle Measure & Two Side Measurements (round to nearest ¼ inch) Partner A 35 o, 4 in, 50 o 95 o, 2 ¼ in, 3 in Partner B 35 o, 4 in, 50 o 95 o, 2 ¼ in, 3 in Activity #3 Summary of classroom discussion: Conclusions about Triangle Congruence: SSS SAS ASA