Questions and Answers
Which similarity statements are true? (Select all that apply)
What is the value of x?
6.6
What is the length of segment DE?
16.2
What is the value of a?
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What is the value of q?
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What is the value of s?
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What is the value of k?
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What is the length of the altitude of an equilateral triangle with sides of 8 units?
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What is the length of side TS?
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In a proof of the Pythagorean theorem using similarity, what allows you to state that the triangles are similar?
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What are two different ways to find the value of a? Explain these methods.
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Study Notes
Similarity Statements in Triangles
- True similarity statements: △JKL ~ △KML, △JMK ~ △JKL, △JMK ~ △KML.
- Statements indicate triangles share the same shape but may differ in size.
Solving for x and Segments
- Given equation: 5/9 = 9/(2x + 3).
- Another equation: 10x + 15 = 9(9).
- x value found to be 6.6.
- Length of segment DE calculated to be 16.2.
Value Determination
- Value of variable a remains unspecified (not provided).
- Value of variable q also not provided (not specified).
- Value of variable s is determined to be 17.
- Value of variable k is identified as 2.
Triangle Properties
- Each side of an equilateral triangle measures 8 units.
- Need to calculate the length of the altitude, information for altitude provided as B (pending further context).
Length of Triangle Side
- Length of side TS is indicated with a value of B (pending further context).
Pythagorean Theorem and Similarity
- Right triangle altitude theorem facilitates establishing similarity between triangles.
- This theorem is critical for forming proportions like c/a = a/f and c/b = b/e.
Methods for Finding 'a'
- First method: Apply the Pythagorean theorem, hypotenuse is 25 units (9 + 16) and one leg is 15 units.
- Second method: Utilize the geometric mean theorem, relating hypotenuse to its legs via proportions (25/a = a/6).
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Description
Test your understanding of right triangle similarity with this assignment flashcard quiz. Check the truth of similarity statements, solve for variables, and find segment lengths. Great for reinforcing concepts in geometry.
