Quiz – Pythagoras Theorem – Visual Proof 1

Test your understanding of the visual proof of the Pythagorean Theorem, including right triangles, areas, and the formula:

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

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

Question 1

What type of triangle is used in the Pythagorean Theorem?

a) Any triangle
b) Right triangle
c) Isosceles triangle

Question 2

Which side is the hypotenuse?

a) Shortest side
b) Side opposite \(90^\circ\)
c) Any side

Question 3

What is the formula?

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

Question 4

What is the area of the large square?

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

Question 5

What is the area using triangles and square?

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

Question 6

What is the area of one right triangle with legs \(a\) and \(b\)?

a) \(ab\)
b) \(\frac{1}{2}ab\)
c) \(2ab\)

Question 7

What is the total area of the four identical right triangles?

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

Question 8

Which expression is equal to:

\((a+b)^2\)

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

Question 9

In the equation:

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

what do we cancel from both sides?

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

Question 10

Suppose the right triangles have sides:

\(a=3,\quad b=4,\quad c=5\)

What is the area of the large square?

a) \(25\)
b) \(49\)
c) \(81\)

Answers

b) Right triangle
b) Side opposite \(90^\circ\)
b) \(a^2 + b^2 = c^2\)
b) \((a + b)^2\)
c) \(c^2 + 2ab\)
b) \(\frac{1}{2}ab\)
b) \(2ab\)
c) \(a^2+2ab+b^2\)
b) \(2ab\)
b) \(49\)

Mulkek