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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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Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
For the right triangle below: $BC^2 = AB^2 + AC^2$

Which equation is equivalent to the above equation?

1. $BC = AB + AC$
2. $AB^2 = BC^2 - AC^2$
3. $AC^2 = BC^2 + AB^2$
4. $AB^2 = BC^2 + AC^2$
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; $angB$ is a right angle; line BD is perpendicular to AC

Which reason explains the following:

$(AC)/(BC) = (BC)/(DC); (AC)/(AB)=(AB)/(AD)$

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. $l eg^2 - "hypotenuse"^2 = l eg^2$
2. $l eg^2 + "hypotenuse"^2 = l eg^2$
3. $l eg^2 - l eg^2 = "hypotenuse"^2$
4. $l eg^2 + l eg^2 = "hypotenuse"^2$
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Which correctly states the Pythagorean Theorem for the triangle shown?
1. $AC^2 + BC^2 = AB^2$
2. $AB^2 + BC^2 = AC^2$
3. $AC^2 + AB^2 = BC^2$
4. none of the above
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
Grade 8 Pythagorean Theorem and Applications CCSS: 8.G.B.6
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