UNIT F: PROPERTIES AND ATTRIBUTES OF
TRIANGLES
Objectives


SWBAT use the Pythagorean Theorem to find
missing sides in right triangles.
SWBAT use the Pythagorean Theorem and the
Pythagorean Inequalities Theorem to classify
triangles.
Unit F:
Properties
and
Attributes
of
Triangles
• The Pythagorean
Theorem
• Finding missing sides
in right triangles
• Is a triangle a right
triangle?
• The Pythagorean
Inequalities Theorem
• Is a triangle an acute
triangle?
• Is a triangle an
obtuse triangle?
Reminders


There is a YouTube lesson to accompany this packet. Go to
http://www.richmath.org/ to see it.
If you need me, please feel free to email me at [email protected], or to
contact me at (443) 375-3331.
The Pythagorean Theorem
Example 1: Find the missing side.
a 2  b2  c2 
62  42  x 2 
36  16  x 2
52  x 2
x  52
 4  13 
 4 13
 2 13 
Geometry Honors
p. 1 of 5
F-7: The Pythagorean Theorem
Last Modified: Friday, March 17, 2017, 1:35 PM
Example 2: Find the missing side.
a 2  b2  c2 
a 2  122
 152 
a 2  144
 225
a 2  81
a  81
9
The Converse of the Pythagorean Theorem
Example 3: Classify the triangle.
The triangle with sides 8, 11, and 13 is…
 Check that it is a triangle using the Triangle Inequality Theorem:
8  11  13 and 8  13  11 and 11  13  8 .
Yes, it is a triangle, so let’s continue.
 Use the Converse of the Pythagorean Theorem to determine whether it is a
right triangle:
a 2  b2  c2
82  112  132
64  121  169
185  169
No, it is not a right triangle.
Geometry Honors
p. 2 of 5
F-7: The Pythagorean Theorem
Last Modified: Friday, March 17, 2017, 1:35 PM
Example 4: Classify the triangle.
The triangle with sides 6, 8, and 10 is…
 Check that it is a triangle using the Triangle Inequality Theorem:
6  8  10 and 6  10  8 and 8  10  6 .
Yes, it is a triangle, so let’s continue.
 Use the Converse of the Pythagorean Theorem to determine whether it is a
right triangle:
a 2  b2  c2
62  82  102
36  64  100
100  100
It is a right triangle.
Pythagorean Inequalities Theorem
Example 5: Classify the triangle.
The triangle with sides 8, 11, and 13 is…
 Check that it is a triangle using the Triangle Inequality Theorem:
8  11  13 and 8  13  11 and 11  13  8 .
Yes, it is a triangle, so let’s continue.
 Use the Converse of the Pythagorean Theorem:
?
c2  a 2  b2
?
132  82  112
?
169  64  121
169  185
Because c2  a 2  b2 , these sides form an acute triangle.
Geometry Honors
p. 3 of 5
F-7: The Pythagorean Theorem
Last Modified: Friday, March 17, 2017, 1:35 PM
Example 6: Classify the triangle.
The triangle with sides 5.8, 9.3, and 15.6 is…
 Check that it is a triangle using the Triangle Inequality Theorem:
5.8  9.3  15.6  15.1  15.6 … ok, no, these sides don’t make a triangle.
Geometry Honors
p. 4 of 5
F-7: The Pythagorean Theorem
Last Modified: Friday, March 17, 2017, 1:35 PM
Classwork
Use the Pythagorean Theorem to find the value of the side x.
1.
2.
3.
4.
Do the following sides make triangles? If so, are they acute, right, or obtuse?
5. 15, 18, 20
6. 7, 8, 11
7. 6, 7, 3 13
Geometry Honors
p. 5 of 5
F-7: The Pythagorean Theorem
Last Modified: Friday, March 17, 2017, 1:35 PM