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Download Triangle Similarity Shortcuts Notes and Practice
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Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Triangle Similarity Shortcuts Notes and Practice AA Triangle Similarity Theorem If two angles of one triangle are ________________________ to two angles of another triangle, then the triangles are ____________________. If Then E R D M L Proving the AA Similarity Theorem: Given: β π΄ β β πΆπ΅π·, β πΆ β β πΆ Prove: βπ΄πΆπΈ~ βπ΅πΆπ· A C B D E A 1 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: SAS Triangle Similarity Theorem If two triangles have ________________ pairs of proportional side lengths and the ____________________ angles are ________________________, then the triangles are similar. If Then E R D M L A Prove the SAS triangle similarity theorem. !" !" Given: = , β πΆ β β πΆ !" !" Prove: βπ΄πΆπΈ~ βπ΅πΆπ· C B D E A 2 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: SSS Triangle Similarity Theorem If two trianlges have __________________ ______________ pairs of side lengths proportional, then the triangles are _________________. If Then E R D M L A Examples: Directions: Determine whether the two triangles are similar. If so, write a similarity statement and list the similarity shortcut. If not, explain why not. 1. 2. Directions: Use the similarity Statements to find the missing measure in each pair of figures. 3. βπΏπΎπ½~βπ ππ 4. βπππ~βπ΅ππΆ 3 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: You Try Directions: Determine whether the two triangles are similar. If so, write a similarity statement and list the similarity shortcut. If not, explain why not. 1. 2. 3. 4. Directions: Use the similarity Statements to find the missing measure in each pair of figures. 5. βπππ~βπΎπΏπ 6. βπππ ~βπππ 4 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Homework 72 Complete pages 605-β607 #2, 5, 7, 8, 9, 10 and the following problems: Directions for Problems 1 & 2: The figures below show 2 similar triangles. For each one: a. Redraw the triangles separately (not overlapping) and label them. b. Write a similarity statement for the two triangles. c. State the similarity shortcut and the similarity ratio. d. Find the missing measures. 1. A 6 cm 8 cm x B 4 cm y E D C 12 cm 2. M z R 5 in x 3 in N Q P y 9 in 5 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Directions for 3-β 6: Determine whether the two triangles are similar. If so, write a similarity statement and list the similarity shortcut. If not, explain why not. 3. 4. 5. 6. 7. At the playground at Pizza Bobβs there are two slides into the ball pit, one small and one large. Both slides make the same angle with the ground. The large slide is 15 feet long, and its top is 10 feet off the ground. The small slide is 8 feet long. a. Draw and label a diagram of both slides. b. How far off the ground is the top of the small slide? Justify your answer. Donβt forget to complete pages 605-β607 #2, 5, 7, 8, 9, 10 6