Algebra 1
Pre-Assessment Pythagorean Theorem
Part I
Name______________________ Date_________ Core______ Score___/20
Read each question carefully and think about the answer before writing your response. Be sure to show on all
problems and round your answers to the nearest hundredth. Calculators are allowed on Part I of the assessment.
1. 8.G.B.6 (4 pts) Determine whether the following numbers could be the sides of a right triangle. Show
your work. If the lengths do create a triangle what type of triangle they create?
a) 3, 5, 4
b) 10, 16, 8
2. 8.G.B.8 (4 pts) Aaron leaves the house to go to school. He walks 10 blocks west and 12 blocks north.
Calculate how far he is from the starting point.
3. 8.G.B.7 (4 pts) Austin asked Jeremy how far from the building the base of the ladder was. Jeremy did
the problem and showed his work below. Austin was sure that Jeremy did something wrong. Who is
right? If Austin is right, what is wrong with Jeremy’s reasoning?
9 • 9 = 81
16 • 16 = 256
81 + 256 = 337
The square root of 337  18.36.
16 ft
The base of the ladder is 18.36 feet from the house.
9 ft
4. 8.G.B.7 (4 pts) Find the length of the hypotenuse.
a) 52 + 42= c2
b) 62 + 82= c2
5. 8.G.B.7 (4 pts) Find the length of the third side of each right triangle.
a)
22
18
a
b)
20
b
25
Algebra 1
Pre-Assessment Pythagorean Theorem
Part II
Name______________________ Date_________ Core______ Score___/28
Read each question carefully and think about the answer before writing your response. Be sure to show on all
problems and round your answers to the nearest hundredth. Calculators are not allowed on Part II of the
assessment.
1. 8.G.B.7 Below is a sequence of squares.
a) (20 pts) Complete the table below relating the side length, x, to the length of the diagonal, y.
Calculate the y value using the digit-by-digit method to find square roots.
x
y
x, side length
y, diagonal length
1
2
3
4
5
b) 8.F.B.4 (4 pts) Graph the points from the table.
c) 8.F.B.5 (4 pts) What do you notice about the points on the graph? Do you see any patterns?