Book Section 7-2Online 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

a

b

c

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

Fun Fact:

If you multiply each number in a

Pythagorean Triple by the same

whole number, the three numbers

that result also form a

Pythagorean Triple.

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

2100 c

10 = c

Let’s Practice

• Find x. Leave your answer in simplest radical form

33b

a2 + b2 = c2

42 + b2 = 72

16 + b2 = 49

b2 = 332 33b

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?

12

35

Phil

* Allentown

122 + 352 = c2

144 + 1225 = c2

1369 = c2

21369 c

37 = c

Let’s Practice

• Find the area of the shaded region.

6 28A6

8h

28b

a2 + b2 = c2

62 + b2 = 82

36 + b2 = 64b2 = 28

2 28b

A = ½ bhA = ½ (12)

1(12)( 28)2

A

212 7A cm

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 = c2

152 + 82 = 212

225 + 64 = 441

289 = 441

289 < 441

289 < c2

OBTUSE

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 cmB. 28cmC. 40cmD. 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