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Mathematics |

Posted Fri Dec 10 15:52:52 PST 1999 by Shai McGowan (with initial help from Mrs. Booth) (slm12@scasd.k12.pa.us).

State College Area High School, State College, Pennsylvania, USA

Materials Required: Signs with letters, worksheets #1 and #2 (see below in lesson), Patty or Wax paper (3 per student),

Activity Time: 2 class periods (standard 47 minutes)

Concepts Taught: Special Segments of Triangles

Lesson Objectives:1. The students will be able to identify the special segments of triangles, the median, angle bisector, altitude, and perpendicular bisectors.

2. The students will be able to locate the point of concurrency among the median, angles bisector, altitude, and perpendicular bisectors in an acute, right, and obtuse triangle.

3. The students will use the strategy of jigsawing to help other members of the group to learn a particular concept.

Prior Knowledge:1. The students will need to be introduced to the definitions of the special segments of a triangle and the point of concurrency.

2. The students will need to be able to use a compass and protractor.

Lesson:

1. The teacher will divide the class up into groups of four students. After deciding how many groups there are, the teacher will pick that many letters from the alphabet. For the sake of the lesson, this teacher will have 6 groups of 4, and will choose letters A-F. The teacher will randomly assign each student a letter. It is important that the teacher chooses the groups randomly. There will be a more diverse group of students. After the students are given a letter, they will be asked by the teacher to get into their groups. The teacher will have placed posters with each letter around the room in areas, to help facilitate the gathering in groups.

2. Once the students are in the letter groups, the teacher will ask each group member to pick a number between 1-4. There should only be one number per group. The teacher will have previously assigned each special segment a number. The teacher will not tell the students which number is assigned to which segment. After the group members have picked a number, the teacher will assign each number a special segment. For instance, all number 1's are perpendicular bisectors, all number 2's are medians, all number 3's are angle bisectors, and all number 4's are altitudes.

3. The teacher will distribute each student three pieces of patty (or wax) paper and a dark crayon. The patty paper should be about a 4 x 4 square or so.4. The teacher will describe the procedure of the activity:

1. Once time is told, each group member will form new groups with other students that have the same number as he. All 1's should be together, all 2's should be together, so forth.

2. Once you are in your new groups, you will draw on your patty paper one acute triangle, one obtuse triangle, and one right triangle. Make all triangles scalene as well.

3. For each triangle, you are to fold your patty paper so that you construct the three special segments you have been assigned. You may use your notes, each other, and your book to help you decide how to do this.

4. You will complete the worksheet for your special segment. (see Attachment #1 below)

5. Pay particular attention to where the three segments are concurrent. Discover any special properties about this point using your protractor, ruler, and compass. (This may be all that is accomplished the first day of the activity.)

6. When time is called, you will return to your groups to teach each of you other original group members what you discovered about your special segment. You must be able to teach the special segment. Your group will be counting on your part to do so.

7. Once all group members are finished, you will complete another worksheet that will require you to use your protractor, compass, or ruler to construct each special type of segment. These must contain the appropriate markings. (see Attachment #2 below)

8. Your letter group will staple the individual patty paper to each individual special segment worksheet and then paper clip all papers to the last worksheet. All work needs to be put in the basket on my desk.5. The teacher will then give the okay to separate into the number group and begin working.

6. The remainder of the time, the teacher will act as a coach. The teacher will use questioning skills to help the groups figure out how to fold the triangles into the special segments and to discover the special properties.

7. When the entire activity is finished, the teacher should dialogue with the students on how they felt after completing the activity.8. On subsequent days, the teacher will allow the individual groups or members to help demonstrate the discoverings as she/he reviews the special segments.

9. Assignment is assigned based on the individual teachers ideas.

________________________________________________________________________

ATTACHMENT #1Geometry Name:

Section 5.2-5.3 Investigation

Angle BisectorsIn your groups, each person is to do the following investigation and be able to report back to your original groups to share your findings.

1. Draw an acute, scalene triangle on your paper.

2. Fold your paper to construct the angle bisectors of each angle.

3. What do you observe about the folds? Write down your findings in if-then form.

4. Draw an obtuse triangle and repeat steps 2 and 3.

5. Where is the point of intersection of all 3 angle bisectors of your acute triangle (name the region it is located in)? Where is it located in your obtuse triangle? Where might it be located in a right triangle?6. Test your thoughts on a right triangle and record your results.

7. Choose one of the triangles for further explorations. Recall: The point of concurrency of

the angle bisectors is called the _________________________. Using your compass, protractor, ruler, and straightedge, what is special about this point? Hint: Compare the lengths of the segments, angles, location, etc.

8. Choose another triangle, and test your results. What do you discover? Write a conjecture about your findings.

_______________________________________________________________________ATTACHMENT #2

Special Segments of Triangles Group members:

GeometryYou are to sketch the three special segments for each type of triangle below. Make sure you use all appropriate markings for each. Beside each special segment, write the group member who jigsawed it. Please show all points of concurrency.

Perpendicular Bisectors of a Triangle: ______________________________

DRAW THREE DIFFERENT TRIANGLES HERE.

ALL SCALENE. ONE ACUTE, ONE OBTUSE, ONE RIGHT

Angle Bisectors of a triangle: __________________________________DRAW THREE DIFFERENT TRIANGLES HERE.

ALL SCALENE. ONE ACUTE, ONE OBTUSE, ONE RIGHT

Medians of a triangle: __________________________________________DRAW THREE DIFFERENT TRIANGLES HERE.

ALL SCALENE. ONE ACUTE, ONE OBTUSE, ONE RIGHT

Altitudes of a triangle: ________________________________________

DRAW THREE DIFFERENT TRIANGLES HERE.

ALL SCALENE. ONE ACUTE, ONE OBTUSE, ONE RIGHT