Triangle Similarity Bundle 2012/2014Caryn White 1
Triangle Similarity Bundle By Caryn White Table of Contents Triangle Similarity Bundle... 2 Copy Right Informations:... 3 Triangle Similarity Foldable... 4 Instructions Page... 5 Student version: Inside of foldable... 6 Completed Version: Inside of foldable... 7 Student Version Notebook Size... 8 Proving Triangles Similar... 9 Instructions Page... 10 Sort: All can be proven similar... 11 Flash Cards Back (reverse order for front to back printing)... 12 Includes Triangles with not enough info to prove similar... 13 Flash Cards Back... 14 Student Response Sheet Version A... 15 Student Response Sheet Version B... 16 Pocket for sort... 17 Keys... 18 Cut and Paste: Similarity Statements... 19 Thoughts and Ideas... 20 Right Triangle Similar Figures... 21 Similar Triangles (1)... 22 Similar Triangles (1a)... 23 Similar Triangles (2)... 24 Similar Triangles (2a)... 25 KEY Right Triangle Similar Figures... 26 KEY Similar Triangles (1)... 27 KEY Similar Triangles (1a)... 28 KEY Similar Triangles (2)... 29 Key Similar Triangles (2a)... 30 Walk Around Activity:... 31 2012/2014Caryn White 2
Instructions... 32 Version A... 33 Absent Student Sheet... 43 Student Response Sheet Version A1... 45 Student Response Sheet Version A2... 46 Version B... 47 Student Response Sheet Version B1... 49 Student Response Sheet Version B2... 50 KEYS... 51 Credits... 52 Copy Right Informations: This package is copyrighted 2011/2013 by Caryn White: Caryn Loves Math All rights reserved. Purchase of this unit entitles the purchaser the right to reproduce the pages in limited quantities for classroom use only. You may also duplicate for use in with your students in your special education and English Language Learners support rooms. Duplication for an entire school, an entire school system or commercial purposes is strictly forbidden without written permission from the publisher. Please contact me if you wish to be granted special permission. I can be contacted using the questions section of my TPT store. www.teachersnotebook.com/shop/carynlovesmath Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden and is a violation of the Digital Millennium Copyright Act (DMCA). These items can be picked up in a google search and then shared worldwide for free. 2012/2014Caryn White 3
Triangle Similarity Foldable By Caryn White 2012/2014Caryn White 4
Instructions Page This foldable activity is designed to help student recognize the ways to prove 2 triangles are similar. Each section has a theorem typed out for students along with a diagram. Students must highlight the corresponding portions of the triangle that are used for that theorem. Then they write the given information and a similarity statement. This way when they are doing their assignment they can see how the answers should be written. I have included a full size and a half size foldable. The half size fits nicely if it is glued into their math notebooks. I have also included a completed version. I give my completed version to my classroom paras. This is a great activity to keep kids engaged. I follow this up by using the foldable on some homework problems to teach them how to use it to help them work. I also allow them to use the foldable on test and quizzes. Possible uses Guided Notes Printout for math notebook Review stations How to make: Cut along outside lines Fold paper long ways but not covering the words Triangle Similarity Cut flaps 2012/2014Caryn White 5
Student version: Inside of foldable Angle Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Side Side Side Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar. Side Angle Side Similarity Theorem If the lengths of two sides of one triangle are proportion to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. 2012/2014Caryn White 6
Completed Version: Inside of foldable Angle Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Side Side Side Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar. Side Angle Side Similarity Theorem Triangle Similarity If the lengths of two sides of one triangle are proportion to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. 2012/2014Caryn White 7
Student Version Notebook Size 2012/2014Caryn White 8
Proving Triangles Similar By Caryn White 2012/2014Caryn White 9
Instructions Page As a Sort There are 24 cards. Depending on your needs you can use 12, 18, or all 24 cards. The 12 and 18 cards sets are all triangles that can be proven similar. The 24 card set includes triangles that do have enough information to prove or there is something incorrect (sides are not proportional). I have included an answer sheet for student to record their results. This makes it easier to walk around and check their work. Differentiation A key is proved for all forms of the sort. This activity has been designed to allow for differentiation. Students that are struggling or have learning difficulties can be given the shorter version (12 cards). While the average student plays the 18 card set and the advanced learner can be given the 24 set. As Flash Cards: Print the cards and the answers front to back. I laminate mine for extended use. Students can then quiz each other during class. For Interactive Math Notebook (or Math Journal) I print the sort on colored sheets. Students cut out the square and decide which method can be used to prove the 2 triangles are similar. I have included a pocket for student to place their place cards in. Student glue the pocket into their math notebook and place the flash card in it for later practice. Possible Uses: Bellwork Check for understanding Alternative to Homework Extra Practice Activity for interactive notebook 2012/2014Caryn White 10
Sort: All can be proven similar 1 20 3 4 5 19 7 8 18 10 11 12 2012/2014Caryn White 11
Flash Cards Back (reverse order for front to back printing) AA~ AA~ SAS~ SSS~ SAS~ SAS~ AA~ SSS~ AA~ SSS~ SSS~ SAS~ 2012/2014Caryn White 12
Includes Triangles with not enough info to prove similar 13 15 23 16 17 21 2 9 6 24 22 14 2012/2014Caryn White 13
Flash Cards Back SSS~ AA~ SSS~ SAS~ SAS~ AA~ Not Similar Not Similar Not Similar Not Similar Not Similar Not Similar 2012/2014Caryn White 14
Student Response Sheet Version A Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ 2012/2014Caryn White 15
Student Response Sheet Version B Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ Can t prove similarity Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ Can t prove similarity Name Period First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list the number of the card below. AA~ SAS~ SSS~ Can t prove similarity 2012/2014Caryn White 16
Pocket for sort 2012/2014Caryn White 17
Keys Key to sort using only first 12 cards AA~ 3,7,18,20 SAS~ 1,4,5,10 SSS~ 8,11,19,12 Key to sort using only first 18 cards AA~ 3,7,16,18,20,23 SAS~ 1,4,5,10,17,21 SSS~ 8,11,13,15,19,12 Key using all 24 cards AA~ 3,7,16,18,20,23 SAS~ 1,4,5,10,17,21 SSS~ 8,11,13,15,19,12 Can t prove similarity 2,6,9,14,22,24 2012/2014Caryn White 18
Cut and Paste: Similarity Statements By Caryn White 2012/2014Caryn White 19
Thoughts and Ideas Directions Each page has 6 sets of similar triangles. Students need to identify the similar triangles and write similarity statements. Then, the students will cut and paste the statements onto the triangles. Worksheet 1 & 1a (2 & 2a) use the same triangles but have been set up slightly different. Also the congruence statements are in a different order so you can use both versions with the same students. Differentiation The worksheets 1, 1a, 2 and 2a are designed for differentiation. All sheets are set up similarly so student do not realize they are working at different levels. Students are given the level they are working at. Worksheet 1: Basic level, students are given part of the similarity statement Worksheet 1a: Triangles are separate but students must find the complete similarity statement. Worksheet 2: Next level, triangles overlap and students are given part of the similarity statements Worksheet 2a: Top level, triangles overlap and students must write the complete similarity statement. Alternative: let the student pick the worksheet they feel comfortable with. For Continued Use: Cut of the bottom triangle names (the answers), then laminate the top section. Students can use dry erase markers and answer the problems. You can erase the answer and use again and again. Possible Uses Review Task Math Station (for student that finish work early) Mid-Lesson Practice (check for understanding) End of lesson check for understanding 2012/2014Caryn White 20
Right Triangle Similar Figures Name: Cut and Paste: Write similarity statements to identifying the three similar triangles in each figure. 1. 4. 2. 5. 3. 6. ADB DBA CBD ACD BDC DAC EHF HEG FHG GFH EGH HFE 2012/2014Caryn White 21
Similar Triangles (1) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ ABC ~ 2. 5. ABC ~ ABC ~ 3. 6. ABC ~ ABC ~ EDF FDE DEF EFD DFE FED 2012/2014Caryn White 22
Similar Triangles (1a) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. 2. 5. 3. 6. ABC CAB DEF CBA FDE ACB EDF EDF BCA FED BAC DFE 2012/2014Caryn White 23
Similar Triangles (2) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ ABE ~ 2. 5. ABC ~ ABE ~ 3. 6. ABE ~ ABE ~ DEC CDE ADC DCE EDC DCA 2012/2014Caryn White 24
Similar Triangles (2a) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ 2. 5. 3. 6. ABE CED BEA CAD BAE DCE CBA DEC ABC EAB EDC CDA 2012/2014Caryn White 25
KEY Right Triangle Similar Figures Name: Cut and Paste: Write similarity statements to identifying the three similar triangles in each figure. 1. 4. 2. 5. 3. 6. ADB DBA CBD ACD BDC DAC EHF HEG FHG GFH EGH HFE 2012/2014Caryn White 26
KEY Similar Triangles (1) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ ABC ~ 2. 5. ABC ~ ABC ~ 3. 6. ABC ~ ABC ~ EDF FDE DEF EFD DFE FED 2012/2014Caryn White 27
KEY Similar Triangles (1a) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. 2. 5. 3. 6. ABC CAB DEF CBA FDE ACB EDF EDF BCA FED BAC DFE 2012/2014Caryn White 28
KEY Similar Triangles (2) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ ABE ~ 2. 5. ABC ~ ABE ~ 3. 6. ABE ~ ABE ~ EDC DEC CDE DCE ADC DCA 2012/2014Caryn White 29
Key Similar Triangles (2a) Name: Cut and Paste: Write similarity statements to identifying the similar triangles in each figure. 1. 4. ABC ~ 2. 5. 3. 6. ABE CED BEA CAD BAE DCE CBA DEC ABC EAB EDC CDA 2012/2014Caryn White 30
Walk Around Activity: By Caryn White 2012/2014Caryn White 31
Instructions Directions for instructor This activity is designed to help students work with similar triangles. This activity also gets students up and about. Place the 10 cards on the wall around your room. Students pick any card to begin with. They should write a proportion using corresponding side of similar triangles. After solving for x, they should find the length of the missing side and find the card with the correct answer. Then work the problem on this card. They should continue until they return to the card they started with. Included are 2 version of this activity. One with 10 cards for use as a walk-around activity (with a smaller size for absent students). A shorter version with only 5 cards great for table work, bell work or use as a review. To help with grading, I have included 2 student answer sheets: One has room for students to show their work, and another with just boxes to show the order. Hints and suggestions: Laminate the pages and student can draw on them with dry erase markers. They can highlight the corresponding sides to help them write the proportion needed to solve the problems. When making copies of the shorter version, I use different colored paper. This allows for easier identification when students misplace a piece. Possible Uses Mid-Lesson or End of Lesson Check for understanding Math Station for students that have finished work early Test Review Homework Alternative Bell work Have Fun. Thanks for your purchase. 2012/2014Caryn White 32
Version A 1 Answer from another card 6 2012/2014Caryn White 33
2 Answer from another card 24 2012/2014Caryn White 34
3 Answer from another card 20 2012/2014Caryn White 35
4 Answer from another card 30 2012/2014Caryn White 36
5 Answer from another card 28 2012/2014Caryn White 37
6 Answer from another card 8 2012/2014Caryn White 38
7 Answer from another card 10 2012/2014Caryn White 39
8 Answer from another card 16 2012/2014Caryn White 40
9 Answer from another card 15 2012/2014Caryn White 41
10 Answer from another card 25 2012/2014Caryn White 42
Absent Student Sheet 2012/2014Caryn White 43
2012/2014Caryn White 44
Student Response Sheet Version A1 Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Show work below 2012/2014Caryn White 45
Student Response Sheet Version A2 Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Student Response Sheet Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Student Response Sheet Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. 2012/2014Caryn White 46
Version B 1 2 Answer from another card 16 Answer from another card 24 3 4 Answer from another card 10 Answer from another card 30 2012/2014Caryn White 47
5 Answer from another card 20 2012/2014Caryn White 48
Student Response Sheet Version B1 Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Show work below 2012/2014Caryn White 49
Student Response Sheet Version B2 Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Student Response Sheet Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. Student Response Sheet Name Period Pick a card to start with. Write the number in the 1 st box. Write a proportion for the similar triangle and find the length of the missing side, then locate the card with the correct length. Write the number in the 2 nd box, and then continue until you reach your first card again. 2012/2014Caryn White 50
KEYS Version A - Set of 10 Cards 1 4 7 2 10 3 8 9 6 5 Note: Students may start with any cards; shift the answer to match the starting point. Version B: Set of 5 Cards 1 4 3 2 5 2012/2014Caryn White 51
Credits All graphics were designed by Caryn White except the following. Clip-art from Cover Page Lulu (chalkboard) font 2012/2014Caryn White 52