IM 8.2.8 Lesson: Similar Triangles
Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4, -2, and 10.
First expression:
Second expression:
Third expression:
Create a triangle using three 'pieces of pasta' and angle A. Your triangle must include the angle you were given, but you are otherwise free to make any triangle you like.
After you have created your triangle...
Measure the angles to the nearest 5 degrees using a protractor and record these measurements.
๏ปฟFind two others in the room who have the same angleย ย and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?
How did you decide if they were or were not congruent or similar?
Now use more 'pasta' and angles A,B, and C to create another triangle.
After you have created your triangle...
Measure the angles to the nearest 5 degrees using a protractor and record these measurements.
๏ปฟFind two others in the room who have the same angleย ย and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?
How did you decide if they were or were not congruent or similar?
Here is triangle PQR. Break a new piece of 'pasta', different in length than segment PQ. Move point S to create this new segment.
Now follow these steps using the applet above:
Create another piece of pasta by checking 'piece 2' with one end atย , and make an angle congruent toย . Create another piece of pasta by checking 'piece 3' on top of lineย ย with one end of the pasta atย . Call the point where the two full pieces of pasta meetย . Is your new pasta triangleย similar toย ? Explain your reasoning.
If your broken piece of pasta were a different length, would the pasta triangle still be similar to ? Explain your reasoning.
Quadrilaterals ABCD and EFGH have four angles.
The angles measureย ย andย .ย Do ย and ย have to be similar?
This diagram has several triangles that are similar to triangle DJI.
Three different scale factors were used to make triangles similar toย . In the diagram, find at least one triangle of each size that is similar toย .
Explain how you know each of these three triangles is similar toย .
Find a triangle in the diagram that is not similar toย .