Pythagorean Theorem Proof (Grade 8)

Print Test (Only the test content will print)
Name: Date:

Pythagorean Theorem Proof

1. 
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]
2. 
For the right triangle below: [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]
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]
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
4. 
Given the side lengths of the right triangle below 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.
Right Triangle ABC v2






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]
Acute Triangle Height v3








Become a Help Teaching Pro subscriber to access premium printables

Unlimited premium printables Unlimited online testing Unlimited custom tests

Learn More About Benefits and Options

You need to be a HelpTeaching.com member to access free printables.
Already a member? Log in for access.    |    Go Back To Previous Page