Pythagorean Theorem and Its Converse
Vocabulary
Pythagorean Theorem: a2 + b2 = c2
Converse of the Pythagorean Theorem: whenever
the sum of the squares of two sides of a triangle equals
the square of the third side of a triangle, the triangle is a
right triangle
Right Triangle – a triangle in which one angle is a right angle
Vertex – a point where two or more straight lines meet (a corner)
1. The drawing below shows three squares joined at their vertices to form a right triangle.
12ft
5 ft
o What are the lengths of each side of the right triangle?
Answer:
5ft, 12ft and
13ft
o What is the area of the shaded box below the right triangle?
Answer:
169 ft2
1
2. If a triangle has side lengths of 6, 8, and 10 units, is it a right triangle? Why or why not?
Answer:
Does 62 + 82 = 102?
Yes, it conforms to
the Pythagorean Theorem.
3. As the crow flies, the distance between Austin to Waco - is 95 miles. the distance from
Waco to Houston is 163 miles, and the distance from Houston to Austin is 146 miles. Do
the three cities form a right triangle? Why or why not?
Answer:
No, 952 + 1462 ≠ 1632 and does not
conform to the Pythagorean Theorem.
2
4. Imagine you are locked out of your home, and the only open window is on the 2nd floor,
24 ft. from the ground. To get inside through the window, you need to borrow a ladder
from a neighbor. A big bush is along the edge of the house, so you’ll have to place the
ladder 7 feet from the house. What length of ladder do you need to reach the window?
Answer:
242 + 72 = c2
c= 25 ft
5. Would the ladder length be longer or shorter:
A. If the window was higher?
Answer:
longer
B. If the bush was smaller?
Answer:
shorter
Volunteer Challenge:
Students now it’s your volunteer’s turn! On the Volunteer Challenge page each student in the group will
create their own Pythagorean Theorem question for their volunteer to complete. After the volunteer
completes each question turn the Volunteer Challenge page into your teacher. Don’t forget to include
everyone’s name in the group!
3
Volunteer Challenge!
4