# Pythagorean Theorem Proof (Grade 8)

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## Pythagorean Theorem Proof

1.

Which of the following is a way to state the Pythagorean Theorem?

- [math]l eg^2 - "hypotenuse"^2 = l eg^2[/math]
- [math]l eg^2 + "hypotenuse"^2 = l eg^2[/math]
- [math]l eg^2 - l eg^2 = "hypotenuse"^2[/math]
- [math]l eg^2 + l eg^2 = "hypotenuse"^2[/math]

2.

For the right triangle shown: [math]BC^2 = AB^2 + AC^2 [/math]

Which equation is equivalent to the above equation?

Which equation is equivalent to the above equation?

- [math]BC = AB + AC [/math]
- [math]AB^2 = BC^2 - AC^2[/math]
- [math]AC^2 = BC^2 + AB^2 [/math]
- [math]AB^2 = BC^2 + AC^2 [/math]

3.

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:

[math](AC)/(BC) = (BC)/(DC); (AC)/(AB)=(AB)/(AD)[/math]

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:

[math](AC)/(BC) = (BC)/(DC); (AC)/(AB)=(AB)/(AD)[/math]

- though a point outside a line, there is exactly one line perpendicular to the given line
- 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
- when the hypotenuse and a leg of a right triangle are congruent to corresponding parts of another right triangle, the triangles are congruent
- the sum of the side lengths of any two sides of a triangle are greater then the length of the third side

4.

Given the side lengths of the right triangle are:

AB = 3

AC = 4

BC = 5

1. Draw a square on each side of the triangle.

2. Calculate the area of each square.

3. Add the areas of the squares on sides AB and AC.

4. Describe how your results in step 3 compare to the area of the square on side BC.

AB = 3

AC = 4

BC = 5

1. Draw a square on each side of the triangle.

2. Calculate the area of each square.

3. Add the areas of the squares on sides AB and AC.

4. Describe how your results in step 3 compare to the area of the square on side BC.

5.

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

Prove: [math]AB^2 + BC^2 = AC^2[/math]

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

Prove: [math]AB^2 + BC^2 = AC^2[/math]

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