Download 7.5 The Converse of the Pythagorean Theorem

7.5 The Converse of the Pythagorean
Theorem
Common Core Standards
8. EE.2 Use square root and cube root symbols to represent solutions to
equations of the form x2 = p and x3 = p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots of
small perfect cubes. Know that √2 is irrational.
8. G.6 Explain a proof of the Pythagorean Theorem and its converse.
8. G.7 Apply the Pythagorean Theorem to determine unknown side lengths
in right triangles in real-world and mathematical problems in two and three
dimensions
WARM-UP
Find the missing lengths.
1)
2)
3
6
4
8
3)
9
12
The Converse of the Pythagorean
Theorem
Can you use the Pythagorean Theorem
to determine if a triangle is a right
triangle?
5
3
?
4
NOTES
The Converse of the Pythagorean Theorem: If the
Pythagorean Theorem works on a triangle then the
triangle must be a right triangle.
Examples
Is the triangle a right triangle?
21
16
20
16
?
?
12
12
EXAMPLES
Use the Converse of the Pythagorean Theorem to show
whether it is possible to have a right triangle with legs
of 8 and 12 and a hypotenuse of 15?
NOTES
When all three sides of a right triangle are whole numbers
it’s called a Pythagorean Triple. Similar triples can be
made by multiplying all three sides of a smaller triple by
the same number.
Examples
3 – 4 – 5 is a Pythagorean 5 – 12 – 13 is a Pythagorean
Triple. Find 3 more similar Triple. Find 3 more similar
triples.
triples.
MORE NOTES
Squares and square roots of numbers cancel each other
out.
2
( 5) = 5
2
( 31) = 31
Examples
Is the triangle a right triangle?
7
13
39
?
6
4
?
5
PRACTICE
Is this a right triangle?
Can this be a right triangle?
c
b
7
?
a
If a = 8,b = 15,c = 17
15
?
13
PRACTICE
Use the Converse of the Pythagorean Theorem to show
whether it is possible to have a right triangle with legs
of 3 and 4 and a hypotenuse of 6.
MORE PRACTICE
Is this a right triangle?
c
b
?
a
If a = 28,b = 6,c = 8
FINAL QUESTION
Is this a right triangle?
c
b
?
a
a = 18, b = 24, c = 30