Transcript Geometry - Fayette County Public Schools
Geometry
• Agenda 1. ENTRANCE 2. Go over Tests/Spiral 3. 7-2 The Pythagorean Theorem and its Converse 4. 7-3 Special Right Triangles 5. Practice Assignment 6. EXIT
Chapter 9
(We actually start with 2 sections of Chapter 7.) 7-2 The Pythagorean Theorem and its Converse 7-3 Special Right Triangles
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.
a
2
b
2
c
2
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 – 8, 15, 17 – 7, 24, 25 – 9, 40, 41 Multiples of these triples will work as well, such as 6, 8, 10 and 15, 36, 39.
• Theorems 7-5, 7-6, and 7-7 Converse of the Pythagorean Theorem triangle.
• triangle.
•
c
2
a
2
b
2 triangle.
Example #1
• Find the missing side of the right triangle.
Example #2
• Find the missing side of the right triangle.
Example #3
• Find the missing side of the right triangle.
Example #4
• Find the area of the right triangle.
Example #5
• Find the area of the right triangle.
53cm
Example #6
• What type of triangle are each of the following?
– A. 4, 6, 7 E. 8, 8, 8 – B. 15, 20, 25 – C. 10, 15, 20 – D. 13, 84, 85 F. 16, 48, 50 G. 7, 8, 9 H. 6, 11, 14
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 2 times the length of a leg. 2 45° 45° 90° n n n 2
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 length of the shorter leg. 30° 60° 90° 3
Example #7
• Find the remaining two sides of each figure.
Example #8
• Find the remaining two sides of each figure.
2 3
Example #9
• Find the remaining two sides of each figure.
Example #10
• Find the remaining two sides of each figure.
3 3
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?
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?
Example #13
• A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden.
Example #14
• A rhombus has 10-inch sides, two of which meet to form a 30° angle. Find the area of the rhombus.
• Practice – WB 7-2 # 1, 3, 5, 10, 14-19 – WB 7-3 # 2, 4, 7, 10, 13, 15 • EXIT