Book Section 7-2
Online Unit 1 Lessons 3 & 4
Instruction
• Pythagorean Theorem:
– In a right triangle, the sum of the squares of the
lengths of the legs is equal to the square of the
length of the hypotenuse
a2 + b2 = c2
c
a
b
Instruction
• Pythagorean Triple:
– Set of nonzero whole numbers a, b, and c that
satisfy equation a2 + b2 = c2
• Examples:
– 3, 4, 5
– 5, 12, 13
– 7, 24, 25
Instruction
• 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 lengths
of the other two sides, then the triangle is a right
triangle.
Instruction
• Theorem:
– If the square of the length of the longest side of a
triangle is greater than the sum of the squares of
the lengths of the other two sides, the triangle is
obtuse
If c2 > a2 + b2, then the triangle is obtuse
Instruction
• Theorem:
– If the square of the length of the longest side of a
triangle is less than the sum of the squares of the
lengths of the other two sides, the triangle is
acute
If c2 < a2 + b2, then the triangle is acute
Let’s Practice
• Find x.
a2 + b2 = c2
62 + 82 = c2
36 + 64 = c2
100 = c2
100  c2
10 = c
Let’s Practice
• Find x. Leave your answer in simplest radical form
a2 + b2 = c 2
42 + b2 = 72
16 + b2 = 49
b2 = 33
b2  33
b  33
Let’s Practice
• Allentown is 35 miles North and 12 miles east of
Philadelphia. A train runs on a straight track between
the two towns. How many miles does it cover?
122 + 352 = c2
144 + 1225 = c2
35
* Allentown
1369 = c2
1369  c2
37 = c
Phil
12
Let’s Practice
• Find the area of the shaded region.
a2 + b2 = c 2
62 + b2 = 82
36 + b2 = 64
b2 = 28
b  28
2
6
b  28
8
h
A = ½ bh
A = ½ (12)
A
1
(12)( 28)
2
A  6 28
A  12 7cm2
Let’s Practice
• The lengths of the sides of a triangle are 15, 8,
and 21. Is this a right, acute, or obtuse
triangle?
If it’s a right trianlge:
a2 + b2 = c 2
152 + 82 = 212
225 + 64 = 441
289 = 441
289 < 441
289 < c2
Review
• Pythagorean Theorem:
a2 + b2 = c2
• If c2 < a2 + b2, then the triangle is acute
• If c2 > a2 + b2, then the triangle is obtuse
Follow Up
• Each question is worth 1 extra credit point added to your chapter 1 test
• Submit via webmail with subject heading “7-2 Extra Credit”
1. The lengths of two legs of a right
triangle are 16cm and 30cm. What is the
length of the hypotenuse? Show work
2. The length of the hypotenuse of a
right triangle is 65 yards. The length
of one leg is 25 yards. What is the
length of the other leg? Show work
3. Which is closest to the length of
the diagonal of a square whose
sides measure 20 cm? Show work
A. 20 cm
B. 28cm
C. 40cm
D. 200cm
4. A ladder resting against the side of a building
reaches 32ft up the building. If the ladder is
40ft long, how far from the building is the base
of the ladder? Show work.
5. The following are the lengths of the
sides of three triangles.
Triangle
Side Measurements
∆QRS
9, 12, 15
∆TUV
17, 23, 31
∆WXY
28, 96, 100
Which are right triangles? Show work