Podcast
Questions and Answers
What is the ratio of 3 inches to 4 feet?
What is the ratio of 3 inches to 4 feet?
1:16
What is the ratio of x to y if 2x = 5y?
What is the ratio of x to y if 2x = 5y?
5:2
What is the ratio of x to y if 6/x + 9 = 2/y + 3?
What is the ratio of x to y if 6/x + 9 = 2/y + 3?
3:1
What is the geometric mean of 20 and 5?
What is the geometric mean of 20 and 5?
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What is the geometric mean of 48 and 3?
What is the geometric mean of 48 and 3?
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What is the geometric mean for 2 and 32?
What is the geometric mean for 2 and 32?
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If a school's 50-foot flagpole casts a 75-foot shadow, how long will the shadow be for a 5-foot tall girl standing near the flagpole?
If a school's 50-foot flagpole casts a 75-foot shadow, how long will the shadow be for a 5-foot tall girl standing near the flagpole?
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If A/x = Y/B, what are the means and extremes?
If A/x = Y/B, what are the means and extremes?
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If triangle HCS is similar to triangle PLD, what is HC/HS equal to?
If triangle HCS is similar to triangle PLD, what is HC/HS equal to?
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If DO IT = GO ON, what is GO/IT equal to?
If DO IT = GO ON, what is GO/IT equal to?
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If triangle CAT is similar to triangle DOG and angle C = 70, angle T = x + 12, angle D = 7x, find angle T.
If triangle CAT is similar to triangle DOG and angle C = 70, angle T = x + 12, angle D = 7x, find angle T.
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What are the four ways to prove triangles similar?
What are the four ways to prove triangles similar?
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Study Notes
Ratios
- The ratio of 3 inches to 4 feet is calculated as 1:16.
- To find the ratio of x to y from the equation 2x = 5y, the ratio simplifies to 5:2.
- When the equation ( \frac{6}{x} + 9 = \frac{2}{y} + 3 ) is solved, the ratio of x to y is 3:1.
Geometric Mean
- The geometric mean of 20 and 5 is ±10.
- For the numbers 48 and 3, the geometric mean is ±12.
- The geometric mean for 2 and 32 is ±8.
Proportional Relationships
- A 50-foot flagpole casts a 75-foot shadow; therefore, a 5-foot tall girl will cast a 7.5-foot shadow.
- In the proportion ( \frac{A}{x} = \frac{Y}{B} ), the means are x and Y, while the extremes are A and B.
- For similar triangles, if triangle HCS is similar to triangle PLD, then the ratio ( \frac{HC}{HS} ) equals ( \frac{PL}{PD} ).
Algebraic Equivalence
- Given ( DOIT = GOON ), the ratio ( \frac{GO}{IT} ) translates to ( \frac{DO}{ON} ).
Angle Relationships in Similar Triangles
- For similar triangles CAT and DOG, with angle C = 70 degrees, angle T expressed as ( x + 12 ), and angle D as ( 7x ), angle T can be calculated to be 22 degrees.
Triangle Similarity Criteria
- Four methods to prove triangle similarity include AAA~, AA~, SAS~, and SSS~.
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Description
This quiz covers key concepts from Chapter 8 of Geometry, focusing on ratios and geometric means. Join us to test your understanding of how to find ratios between different measurements and calculate geometric means. Perfect for reviewing important geometric principles!
