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?
What is the geometric mean of 48 and 3?
What is the geometric mean of 48 and 3?
What is the geometric mean for 2 and 32?
What is the geometric mean for 2 and 32?
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?
If A/x = Y/B, what are the means and extremes?
If A/x = Y/B, what are the means and extremes?
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?
If DO IT = GO ON, what is GO/IT equal to?
If DO IT = GO ON, what is GO/IT equal to?
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.
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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