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0.3.12 Angles in a Triangle Lesson Objectives Observe that the sum of the angles in a triangle is 180 degrees. Required Materials geometry toolkits Setup: Can You Draw It? (5 minutes) Students in groups of 2. Quiet work time for 3 minutes to complete the table followed by partner and whole class discussion. Statement Anticipated Responses 1. Complete the table by drawing a triangle in each cell that has the properties listed for its column and row. If you think you cannot draw a triangle with those properties, write “impossible” in the cell. Answers vary. It is possible to draw all of the triangles except equilateral right and equilateral obtuse. 2. Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement. acute (all right (has a obtuse (has an angles acute) right angle) obtuse angle) scalene (side lengths all di erent) isosceles (at least two side lengths are equal) equilateral (three side lengths equal) Setup: Find All Three (10 minutes) Access to geometry toolkits. Distribute one card to each student, making sure that all three cards have been distributed for each triangle. Prepare and display a table for all to see with columns Angle 1, Angle 2, Angle 3 and one row for each group of three students. Statement Anticipated Responses Your teacher will give you a card with a picture of a triangle. The angle combinations are: 40,50,90; 40,60,80; 50,50,80; 20,20,140; 20,40,120. 1. The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles. 2. Find two other students with triangles congruent to yours, but with a different angle labeled. Confirm that the triangles are congruent, that each card has a different angle labeled, and that the angle measures make sense. 3. Enter the three angle measures for your triangle on the table your teacher has posted. Setup: Tear It Up (20 minutes) Access to geometry toolkits. Students in groups of 2. Distribute triangle sheet to each group. 5 minutes group work followed by class discussion. Distribute angle sheet to each group. 5 minutes group work followed by class discussion. Statement Anticipated Responses Your teacher will give you and your partner a printed page with three triangles and a blank space. 1. Answers vary. Sample response: None of the triangles are congruent. 1. Cut the page into two pieces so that one partner has two triangles and one has a triangle and the blank space. Together, decide what kind of triangle to draw in the blank space, and create it. (It should 2. Answers vary. Sample response: The three angles, when put together to form one angle, appear to make a line or a 180 degree angle. My partner had the same result. look different from the other three triangles.) Are any of your triangles congruent? Explain how you know. 2. For each triangle: cut out the triangle, and then tear off the three corners so that you have three angles. Line up two of the angles so that two sides are right next to each other with no gaps, and their vertices touch. This will create a new, larger angle. Line up the third angle with this new angle in the same way. What do you notice about the place where the three angles come together? What is the measure of this new angle? How does your result compare with your partner’s? You and your partner together should do this for all four triangles. Pause for your teacher to check your work. 3. Your teacher will give you a new page. Cut the page into two pieces so that one partner has two sets of angles and one has a set of angles and a blank space. Create a different set of three angles in the blank space. What is the sum of the measures of three angles that make a line? Explain how you know. 3. Answers vary. Sample response:The three angles measures add up to 180 degrees. I can see this by looking at a protractor. 4. Answers vary. Sample response:Yes we both were able to build triangles with different shapes. 4. Cut out each set of three angles. Can you make a triangle that has these same three angles from each set? Setup: Missing Angle Measures (5 minutes) Cool-down (5 minutes) In triangle degrees. , the measure of angle Anticipated Responses is 50 1. Answers vary. Sample responses: 100 and 30, 90 and 40, 80 and 50. 1. Find any two numbers that could be the measures of and in degrees. 2. What could be the measures of angles is . . . a. an acute triangle? and if 2. Answers vary. Sample responses: Acute: 80 and 50. Obtuse: 100 and 30. Right: 90 and 40. b. an obtuse triangle? c. a right triangle? Lesson Summary (5 minutes) What did you notice about the sum of the angles inside a triangle? Is it possible to make a triangle with any combination of three angles?