Similar Triangles Project (Major grade)

Transcription

1 Similar Triangles Project (Major grade) Due 5/1 You will create a picture of a noun with at least 18 triangles (similar triangles) on an 11in X 14in poster board or construction paper. Make sure you include a title of your noun on the top of your poster board. You will be making 6 triangles using AA similarity, 6 triangles using SSS similarity and 6 triangles using SAS similarity You may NOT use the same scale factor for any of the similar triangles that you create. Use the handouts on the blog to create your similar triangles. You will have to turn in the handouts, so PHOTOCOPY onto white or colored paper your triangles to design your noun poster. If you use white paper, color your triangles using markers or colored pencils. If you want to use more than 18 triangles you may reuse any of the triangles you have created but you may not make new triangles. Write a paragraph that: o Defines each of the triangle similarities (AA, SSS, SAS). o Describes the difference between triangle similarity and triangle congruence o Describe what happens to your new triangles when you multiply your original triangle by a scale factor less than one and greater than one. o Explain why your calculations of proportions and the sum of angle measurements might not be exact. o Explain any difficulties that your many have had with this project and if this project helped you understand triangle similarity. Rubric Points Picture is a noun with at least 18 triangles / 10 Triangles are neatly colored, cut and glued to an 11x14 poster board / 20 Triangles are neatly drawn on the paper provided. The measurements of the lengths of the sides are given in centimeters and the angle measurements are given. / 15 Calculations are accurate / 25 Similarity statement, scale factor and sum of angles are provided. / 20 Paragraph written. / 10 TOTAL: / 100

2 AA Similarity Name Step 1: Create a line segment. Label the endpoints A and B. Measure in centimeters (cm). Step 2: From point A, use your protractor to measure an acute angle (you choose the angle measurement) and make a point. Label the angle with the measurement. Draw a line from point A through the new point. Step 3: Repeat Step 2 from point B. Step 4: Where the 2 new lines intersect is point C. You should now have a triangle. Step 5: Measure the sides of the triangle in cm. Step 6: Create a second triangle that is similar to the first one that you created. Start with a line segment that is different than the original and repeat steps 2-5. Call this triangle A B C. Step 7: Create a third triangle that is similar to the first one that you created. Start with a line segment that is different than the first 2 triangles and repeat steps 2-5 again. Call this triangle A B C. Step 8: Start all over from step 1 to create a second set of 3 triangles but call these triangles XYZ, X Y Z and X Y Z. Step 9: Provide a similarity statement. Step 10: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to the new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that are equal to each other (or very close!) Step 11: Add all 3 angle measurements. Don t just give your answer; make sure you show the angle measures. Triangles ABC, A B C and A B C

3 Triangles XYZ, X Y Z and X Y Z AA Similarity Name

4 SSS Similarity Name Step 1: Create a triangle. Measure and label the sides in cm. Label the vertices of the triangle CAT Step 2: Choose a scale factor that is less than 1. Step 3: multiply each side of the triangle by the scale factor. Step 4: Create a new triangle with your new side measurements. Call your new triangle C A T. (hint- it might help to measure one angle from your original triangle. Use the same angle measurement on the corresponding angle of your new triangle to help draw your new triangle. Step 5: repeat steps 2-4 but this time use a scale factor that is greater than 1. Name your triangle C A T. Step 6: Repeat steps 1-5 for your second set of triangles using SSS similarity. Side lengths must be different. Name your triangles DOG, D O G and D O G. Step 7: Provide a similarity statement. Step 8: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to the new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that are equal to each other (or very close!) Step 9: Provide the sum of the angle measures. Triangles CAT, C A T, C A T

5 Triangles DOG, D O G, D O G SSS Similarity Name

6 SAS Similarity Name Step 1: Create a line segment. Label the endpoints P and G. Measure in centimeters (cm). Step 2: From point P, use your protractor to measure an acute angle (you choose the angle measurement) and make a point and name the point I. Label the angle with the measurement. Draw a line from point P to point I. Measure the line segment PI in cm. Step 3: Create a triangle by connecting point I and point G. Measure the line segment IG in cm. Step 4: Choose a scale factor that is less than 1. Step 5: Multiply segments PG and PI by the scale factor, this with be the lengths of segments P G and P I. Draw segment P G first. From point P and using the same angle measurement that you chose from step 2 to create segment P I. Step 6: Create your new triangle P I G by connecting points I and G. Measure segments I G. Step 7: repeat steps 2-6 but this time use a scale factor that is greater than 1. Name your triangle P I G. Step 8: Start all over from step 1 to create a second set of 3 triangles but call these triangles RAT, R A T and R A T. Step 9: Provide a similarity statement. Step 10: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to the new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that are equal to each other (or very close!). Step 11: Add all 3 angle measurements. Don t just give your answer; make sure you show the angle measures. Triangles PIG, P I G, P I G

7 Name Triangles RAT, R A T, R A T