1. Bellringer
Simplify each expression
5 ∙ 10
243
6 ∙ 8

2. 7-2 The Pythagorean Theorem and Its Converse

3. Pythagorean Theorem (Thm
Pythagorean Theorem (Thm. 7-4): 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.

4. Pythagorean Theorem
𝑎 2 + 𝑏 2 = 𝑐 2
Leg
Leg
Hypotenuse

5. Pythagorean Triple: set of nonzero whole numbers, a, b, and c that satisfy the Pythagorean Theorem
Common Triples:
3, 4, 5 5, 12, 13
7, 24, 25 8, 15, 17
12, 25, , 21, 29

6. 𝑎 2 + 𝑏 2 = 𝑐 2
8 2 + 𝑏 2 = 12 2
64+ 𝑏 2 =144
𝑏 2 =80
𝑏 2 = 80
𝑏=4 5

7. Bellringer
Find the value of x x 12 12 x 15 8

8. 𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2
62, ,500= 𝑐 2
185,000= 𝑐 2
185,000 = 𝑐 2
185,000 =𝑐 𝑐=
𝑐≈430𝑚

9. Use the Pythagorean Thm. to find the height first!
Finding the Area using the Pythagorean Theorem
Use the Pythagorean Thm. to find the height first!
12 m
12 m
ℎ 2 = 12 2
100+ ℎ 2 =144
ℎ 2 =44
ℎ 2 = 44
ℎ=2 11
20 m
𝐴=𝑏ℎ
𝐴= 1 2 (20)(2 11)
𝐴=20 11

10. Converse of the Pythagorean Theorem (Thm
Converse of the Pythagorean Theorem (Thm. 7-5): 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.

11. 𝑎 2 + 𝑏 2 = 𝑐 2
= 7 2
16+36=49
52≠49
Since the sum of the square of
the legs is not equal the
square of the hypotenuse, this
cannot be a right triangle.

12. 𝑎 2 + 𝑏 2 = 𝑐 2
= 85 2
169+7,056=7,225
7,225=7,225
Since the sum of the square of
the legs is equal to the square
of the hypotenuse, this is a right
triangle.

13. Theorem 7-6:
Theorem 7-7:

14. Since the square of the hypotenuse
The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right.
𝑐 2 = 𝑎 2 + 𝑏 2
14 2 =
196=36+121
196=157
196>157
Since the square of the hypotenuse
is greater than the sum of the square
of the legs, the triangle is an obtuse
triangle.

15. Since the square of the hypotenuse is less than the sum of the square
The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right.
𝑐 2 = 𝑎 2 + 𝑏 2
15 2 =
225=
225=313
225<313
Since the square of the hypotenuse
is less than the sum of the square
of the legs, the triangle is an acute
triangle.

16. Assignment
Pg. 361 #’s 2 – 34 even