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Common Core Standard 8.G.B.6 Questions

Explain a proof of the Pythagorean Theorem and its converse.

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None Social Sciences CCSS: 8.G.B.6
What is validity?
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
For the right triangle shown: [math]BC^2 = AB^2 + AC^2 [/math]

Which equation is equivalent to the above equation?
Right Triangle ABC v1
  1. [math]BC = AB + AC [/math]
  2. [math]AB^2 = BC^2 - AC^2[/math]
  3. [math]AC^2 = BC^2 + AB^2 [/math]
  4. [math]AB^2 = BC^2 + AC^2 [/math]
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Write the letter "D" at the point where the altitude meets line AC.

Given: Triangle ABC is a right triangle; [math]angB[/math] is a right angle; line BD is perpendicular to AC

Which reason explains the following relationships?

[math](AC)/(BC) = (BC)/(DC); (AC)/(AB)=(AB)/(AD)[/math]
Acute Triangle Height v3
  1. though a point outside a line, there is exactly one line perpendicular to the given line
  2. given the altitude of a right triangle, the legs are the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg
  3. when the hypotenuse and a leg of a right triangle are congruent to corresponding parts of another right triangle, the triangles are congruent
  4. the sum of the side lengths of any two sides of a triangle are greater then the length of the third side
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Which of the following is a way to state the Pythagorean Theorem?
  1. [math]l eg^2 - "hypotenuse"^2 = l eg^2[/math]
  2. [math]l eg^2 + "hypotenuse"^2 = l eg^2[/math]
  3. [math]l eg^2 - l eg^2 = "hypotenuse"^2[/math]
  4. [math]l eg^2 + l eg^2 = "hypotenuse"^2[/math]
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Which correctly states the Pythagorean Theorem for the triangle shown?
Right Triangle ABC v3
  1. [math]AC^2 + BC^2 = AB^2[/math]
  2. [math]AB^2 + BC^2 = AC^2[/math]
  3. [math]AC^2 + AB^2 = BC^2[/math]
  4. none of the above
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Which of the following side lengths satisfy the requirements for a right triangle?
  1. 1, 2, 3
  2. 3, 5, 8
  3. 7, 10, 12
  4. 9, 12, 15

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