1. Geometry Agenda 1. ENTRANCE 2. Go over Tests/Spiral
The Pythagorean Theorem and its Converse
Special Right Triangles
5. Practice Assignment
6. EXIT

2. Chapter 9 7-2 The Pythagorean Theorem and its Converse
(We actually start with 2 sections of Chapter 7.)
7-2 The Pythagorean Theorem and its Converse
7-3 Special Right Triangles

3. Theorem 7-4 The 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.

4. Common Pythagorean Triples
Certain sets of three numbers appear often in Geometry problems since they satisfy the Pythagorean Theorem.
3, 4, 5
5, 12, 13 Multiples of these triples
8, 15, 17 will work as well, such as
7, 24, , 8, 10 and 15, 36, 39.
9, 40, 41

5. Theorems 7-5, 7-6, and 7-7 Converse of the Pythagorean Theorem
If , then the triangle is a right triangle.
If , then the triangle is an obtuse triangle.
If , then the triangle is an acute triangle.

6. Example #1
Find the missing side of the right triangle.

7. Example #2
Find the missing side of the right triangle.

8. Example #3
Find the missing side of the right triangle.

9. Example #4
Find the area of the right triangle.

10. Example #5
Find the area of the right triangle.

11. Example #6 What type of triangle are each of the following?
A. 4, 6, 7 E. 8, 8, 8
B. 15, 20, 25 F. 16, 48, 50
C. 10, 15, 20 G. 7, 8, 9
D. 13, 84, 85 H. 6, 11, 14

12. Theorem 7-8 45°-45°-90° Triangle Theorem
In a 45°-45°-90° triangle, both legs are congruent and the length of the hypotenuse is
times the length of a leg.
45° 45° 90°
n n n

13. Theorem 7-9 30°-60°-90° Triangle Theorem
In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg.
30° 60° °
n n n

14. Example #7
Find the remaining two sides of each figure.

15. Example #8
Find the remaining two sides of each figure.

16. Example #9
Find the remaining two sides of each figure.

17. Example #10
Find the remaining two sides of each figure.

18. Example #11
A square garden has sides 100 ft long. You want to build a brick path along a diagonal of the square. How long will the path be?

19. Example #12
The distance from one corner to the opposite corner of a square playground is 96 ft. How long is each side of the playground?

20. Example #13
A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden.

21. Example #14
A rhombus has 10-inch sides, two of which meet to form a 30° angle. Find the area of the rhombus.

22. Practice
WB 7-2 # 1, 3, 5, 10, 14-19
WB 7-3 # 2, 4, 7, 10, 13, 15
EXIT