Right Triangle Similarity Assignment

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Questions and Answers

Which similarity statements are true? (Select all that apply)

  • â–³JKL ~ â–³KML (correct)
  • â–³JMK ~ â–³JKL (correct)
  • â–³JMK ~ â–³KML (correct)
  • None of the above

What is the value of x?

6.6

What is the length of segment DE?

16.2

What is the value of a?

<p>A</p> Signup and view all the answers

What is the value of q?

<p>B</p> Signup and view all the answers

What is the value of s?

<p>17</p> Signup and view all the answers

What is the value of k?

<p>2</p> Signup and view all the answers

What is the length of the altitude of an equilateral triangle with sides of 8 units?

<p>B</p> Signup and view all the answers

What is the length of side TS?

<p>B</p> Signup and view all the answers

In a proof of the Pythagorean theorem using similarity, what allows you to state that the triangles are similar?

<p>The right triangle altitude theorem</p> Signup and view all the answers

What are two different ways to find the value of a? Explain these methods.

<p>You could use the Pythagorean theorem or the geometric mean (leg) theorem.</p> Signup and view all the answers

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Study Notes

Similarity Statements in Triangles

  • True similarity statements: â–³JKL ~ â–³KML, â–³JMK ~ â–³JKL, â–³JMK ~ â–³KML.
  • 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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