Quiz – Pythagoras Theorem – Visual Proof 2

Test your understanding of the second visual proof of the Pythagorean Theorem using areas, squares, and right triangles.

\(a^2 + b^2 = c^2\)

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

What type of triangle is used in this proof?

a) Any triangle
b) Right triangle
c) Equilateral triangle

Question 2

How many triangles are used?

a) \(2\)
b) \(3\)
c) \(4\)

Question 3

What is the side of the large square?

a) \(a\)
b) \(b\)
c) \(a + b\)

Question 4

What is inside the first shape?

a) Square \(c\)
b) Squares \(a\) and \(b\)
c) No squares

Question 5

What is inside the second shape?

a) Square with side \(c\)
b) Rectangle
c) Triangle

Question 6

What is the total area of the two squares in the first arrangement?

a) \(a^2+b^2\)
b) \(a+b\)
c) \(2ab\)

Question 7

What is the area of the smaller square in the second arrangement?

a) \(a^2\)
b) \(b^2\)
c) \(c^2\)

Question 8

Why must the areas \(a^2+b^2\) and \(c^2\) be equal?

a) Both arrangements use the same four triangles and the same large square
b) All triangles have the same side lengths as the large square
c) The large square has an area of \(c^2\)

Question 9

What changes between the first and second arrangements?

a) The sizes of the triangles
b) The arrangement of the triangles
c) The side length of the large square

Question 10

If \(a=5\) and \(b=12\)

what is \(c^2\)?

a) \(17\)
b) \(144\)
c) \(169\)

Answers

b) Right triangle
c) \(4\)
c) \(a + b\)
b) Squares \(a\) and \(b\)
a) Square with side \(c\)
a) \(a^2+b^2\)
c) \(c^2\)
a) Both arrangements use the same four triangles and the same large square
b) The arrangement of the triangles
c) \(169\)

Mulkek