Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 4-6 Pythagorean Theorem
Learning Goals: (8) What is the Pythagorean Theorem? For which type of triangles does the
Pythagorean Theorem apply?
Warm Up:
1. Given the following segments, determine if they can form a triangle: Be sure to justify your answer.
a. 12, 16, 20
b. 102, 102, 203
2. Determine which side of the given triangle is the longest:
The Pythagorean Theorem
We can only use the Pythagorean Theorem with right triangles.
Let’s use it so find the missing side of a right triangle.
Remember! “c” is always the hypotenuse, which is opposite the right angle!
Guided Example:
Find the missing side of the
triangle below
1) a = 5, b = 12, c = x (c is always the hypotenuse)
2)
.
c2 = a2 + b2
x2 = 52 + 122
x2 = 25 + 144
x2 = 169
√𝑥 2 = √169
x = 13
Steps:
1) Identify the measure of each side length and
classify them as a, b, or c.
2) Use the Pythagorean Theorem and properties of
Algebra to find the missing side.
3) Put your answer in simplest radical form, if
applicable.
Geometry/Trig
Try one!
1.
Find the missing side. Show all of your work! Keep your answer as a radical.
2. Solve for the length of side BC? Leave your answer in simplest radical form.
Pythagorean Triples
The side lengths that satisfy the Pythagorean Theorem, (a, b, and c) are known as Pythagorean Triples.
There are some common triangle side lengths that we should be familiar with and be able to recognize
when we see them! There are many of them, but see some examples below!
Guided Example:
Show that (3,4,5) is a Pythagorean triple.
Appropriately label the triangle below with these
side lengths.
.
1)
a = 3, b = 4, c = 5
2) 52 = 32 + 42
25 = 9 + 16
25 = 25
3) Yes, this is a Pythagorean triple because the
side lengths satisfy the Pythagorean Identity.
Steps:
1) Identify the measure of each side length and
classify them as a, b, or c.
2) Use the Pythagorean Theorem to see if the left
side equals the right side.
3) Come to a conclusion and justify your answer.
Geometry/Trig
Try one!
1. Which one of the following is NOT a Pythagorean triple?
a. 7, 24, 25
b. 8, 15, 17
c. 9, 12, 15
d. 10, 16, 19
2. Determine whether the given triangle is a right triangle. Explain how you arrived at your answer.
Mixed Practice
3. Does this triangle have a right angle? Explain your answer.
Geometry/Trig
4. Circle the error(s) in the student’s work, then solve for x correctly.
5. If (x, 40, 41) are the sides of a right triangle, where x is the smallest side, what is the value of x?
5) If (16, 30, y) are the sides of a right triangle, where y is the largest side, what is the value of y? Leave your answer
in simplest form.