Download - Guided Notes Converse of Pythagorean Theorem
© Edgenuity, Inc. 1
Warm-Up Converse to the Pythagorean Theorem
? Lesson Question
Lesson Goals
Use the converse of the Pythagorean theorem.Use the converse of the Pythagorean theorem.
Determine whether a triangle is a
triangle.
Apply the converse of the
real-world scenarios.
theorem to
Words to Know
Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you.
substitute
deduce
Pythagorean theorem
converse
right triangle
A. to infer; to draw a conclusion
B. to take the place of; to replace
C. a triangle having an interior angle measuring 90 degrees
D. the theorem stating that the sum of the squares of the lengths of the legs in a right triangle is equal to the square of the length of the hypotenuse
E. statement formed by switching the hypothesis and the conclusion of a conditional
WK2
© Edgenuity, Inc. 2
Warm-Up Converse to the Pythagorean Theorem
Pythagorean Theorem Review
Use the Pythagorean theorem to determine the height of the tree.
• a2 + b2 =
a2 + b2 = c2
a2 + 212 =
a2 + = 1225
−441 −441
a2 =
= 7842a
a = ft
35 ft
21 ft
a
© Edgenuity, Inc. 3
Instruction
2Slide
Converse to the Pythagorean Theorem
Consider the Pythagorean Theorem
Consider the Pythagorean theorem.
• The sum of the squares of the legs in a right triangle is
equal to the of the length of the hypotenuse.
• If a triangle with sides a, b and c is a triangle, then a2 + b2 = c2.
• What can you deduce about a triangle with side lengths 6, 8, and 10?
a
b
c
Using the Converse of the Pythagorean Theorem
Pythagorean theorem
• If a triangle with sides a,
b and c is a
triangle, then a2 + b2 = c2.
to find
side lengths
of the Pythagorean
theorem
• If a triangle has sides a, b and c such that
+ b2 = c2, then
the triangle is a right triangle.
determine if a triangle is a right triangle
© Edgenuity, Inc. 4
Instruction Converse to the Pythagorean Theorem
5Slide
Apply the Converse of the Pythagorean Theorem
EXAMPLE
Is a triangle with lengths 15, 20, and 25 a right triangle?
• Apply the converse by the values into the Pythagorean theorem.
a2 + b2 = c2
152 + = 252
225 + 400 =
625 = 625
Since substituting these sides into the formula resulted in a true statement, the side lengths 15, 20, and 25 do form a right triangle.
20
© Edgenuity, Inc. 5
Instruction Converse to the Pythagorean Theorem
7Slide
Verify the Converse of the Pythagorean Theorem
Verify that 8, 15 and 17 is a Pythagorean triple.
• Does the sum of the squares of the two shorter sides equal the square of the longest side?
a2 + b2 =
+ 152 = 172
64 + = 289
289 = 289
Therefore, this is a right triangle and these numbers are a Pythagorean
.
817
15
225
64
© Edgenuity, Inc. 6
Instruction Converse to the Pythagorean Theorem
9Slide
12
Using the Converse of the Pythagorean Theorem
EXAMPLE
Does a triangle with side lengths 10, 70 , and 30 form a right triangle?
a2 + b2 = c2
70 10
2 22+
=
70 + 30 = 100
= 100
8 70
30 6
< <
< <
Since these three side lengths satisfy the Pythagorean theorem, I know that they
do form a triangle.
Interpret a Real-World Scenario
REAL-WORLD CONNECTION
A window frame appears to be rectangular. The sides of the window frame are 82 inches and 60 inches, while the length of the diagonal is 102 inches. Does the corner of the window frame form a right triangle for the window to be rectangular?
a2 + b2 = c2
+ 822 = 1022
3,600 + =
10,324 ≠ 10,40460
82?
?
© Edgenuity, Inc. 7
Instruction Converse to the Pythagorean Theorem
14Slide
Right Triangle Versus Not Right Triangle
EXAMPLE
Right triangle
• A support on a bridge has sides that measure 2.5 m, 6 m and 6.5 m.
a2 + b2 = c2
2.52 + = 6.52
6.25 + 36 =
42.25 = 42.25
Not right triangle
• A kite has sides that measure 16 in., 18 in. and 24 in.
a2 + b2 = c2
+ 162 = 242
324 + = 576
580 576
?
?
6
6.5
18 16
© Edgenuity, Inc. 8
Summary Converse to the Pythagorean Theorem
Answer
Use this space to write any questions or thoughts about this lesson.
Lesson Question
What is the converse of the Pythagorean theorem and how is it used?
?