Transcript Section 7 * 2 The Pythagorean theorem & Its converse

Section 7 – 2
The Pythagorean theorem
& Its converse
Objectives:
To use the Pythagorean Theorem
To use the Converse of the Pythagorean Theorem
Pythagorean Theorem
2
2
𝑎 +𝑏 =𝑐
2
Used to find a missing side of a RIGHT triangle.
Pythagorean Triple
A set of nonzero whole numbers a, b, and c that
satisfy the Pythagorean Theorem.
3, 4, 5
Common Pythagorean Triples:
5, 12, 13
8, 15, 17
7, 24, 25
If you multiply each number in a Pythagorean Triple by
the same whole number, the three numbers that result
also form a Pythagorean Triple
Example 1
A)
Pythagorean Triples
Find the length of the hypotenuse of
∆ABC. Do the lengths of the sides of
∆ABC form a Pythagorean Triple?
B) A right triangle has a hypotenuse of
length 25 and a leg of length 10. Find the length
of the other leg. Do the lengths of the sides
form a Pythagorean triple?
C) A right triangle has legs of length 16 and
30. Find the length of the hypotenuse. Do the
lengths of the sides form a Pythagorean triple?
Example 2 Using Simplest Radical Form
A) Find the value of x. Leave your answer in
simplest radical form.
B) The hypotenuse of a right triangle has
length 12. One leg has length 6. Find the length
of the other leg. Leave your answer in simplest
radical form.
C) Find the value of x. Leave your answer in
simplest radical form.
Example 3
Real-World Connection
A) The Parks Department rents paddle boats
at docks near each entrance to the park. About
how far is it to paddle from one dock to the
other?
B) How far is home plate from second base
on a baseball diamond?
C) How far is home plate from second base
on a softball diamond?
Textbook Page 360 – 361; #1 – 17
Section 7 – 2
Continued…
Objectives:
To use the Converse of the Pythagorean Theorem
Example 4
A)
Finding Area
Find the area of the triangle.
B)
Find the area of the triangle.
C) The hypotenuse of an isosceles right
triangle has length 20 cm. Find the area.
Converse of the
Pythagorean Theorem
If the square of the length of one side
of a triangle is equal to the sum of the
squares of the other two sides, then
the triangle is a right triangle.
Example 5
Is it a Right Triangle?
Is each triangle a right triangle?
A)
B)
C)
A triangle with side lengths 16, 48, and
50.
Theorem 7 – 6
2
2
2
If 𝑐 > 𝑎 + 𝑏 , the triangle is ________
Theorem 7 – 7
If 𝑐 2 < 𝑎2 + 𝑏 2 , the triangle is ________
Example 6
Classifying Triangles as Acute,
Obtuse, or Right.
The lengths of the sides of a triangle are given.
Classify each triangle as acute, obtuse, or right.
A) 6, 11, 14
B) 12, 13, 15
C) 7, 8, 9
Homework:
7 – 2 Ditto; 1 – 19 Odds