Download Triangle Similarity Shortcuts Notes and Practice

Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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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
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Proving the AA Similarity Theorem: Given: ∠𝐴 ≅ ∠𝐶𝐵𝐷, ∠𝐶 ≅ ∠𝐶 Prove: ∆𝐴𝐶𝐸~ ∆𝐵𝐶𝐷 A
C
B
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A
1 Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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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
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Prove the SAS triangle similarity theorem. !"
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Given: = , ∠𝐶 ≅ ∠𝐶 !"
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Prove: ∆𝐴𝐶𝐸~ ∆𝐵𝐶𝐷 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:
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SSS Triangle Similarity Theorem If two trianlges have __________________ ______________ pairs of side lengths proportional, then the triangles are _________________. If Then E
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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. ∆𝐿𝐾𝐽~∆𝑅𝑄𝑃 4. ∆𝑆𝑈𝑇~∆𝐵𝑈𝐶 3 Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
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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. ∆𝑉𝑈𝑇~∆𝐾𝐿𝑀 6. ∆𝑃𝑄𝑅~∆𝑃𝑉𝑊 4 Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Homework 72 Complete pages 605-­‐607 #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
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B
4 cm
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C
12 cm
2. M
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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-­‐ 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 Bob’s 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. Don’t forget to complete pages 605-­‐607 #2, 5, 7, 8, 9, 10 6