Presentation on theme: "Geometry Agenda 1. ENTRANCE 2. Go over Tests/Spiral"— Presentation transcript:
1 Geometry Agenda 1. ENTRANCE 2. Go over Tests/Spiral The Pythagorean Theorem and its ConverseSpecial Right Triangles5. Practice Assignment6. 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 Converse7-3 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, 55, 12, 13 Multiples of these triples8, 15, 17 will work as well, such as7, 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 #1Find the missing side of the right triangle.
7 Example #2Find the missing side of the right triangle.
8 Example #3Find the missing side of the right triangle.
11 Example #6 What type of triangle are each of the following? A. 4, 6, 7 E. 8, 8, 8B. 15, 20, 25 F. 16, 48, 50C. 10, 15, 20 G. 7, 8, 9D. 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 istimes 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 #7Find the remaining two sides of each figure.
15 Example #8Find the remaining two sides of each figure.
16 Example #9Find the remaining two sides of each figure.
17 Example #10Find the remaining two sides of each figure.
18 Example #11A 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 #12The 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 #13A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden.
21 Example #14A rhombus has 10-inch sides, two of which meet to form a 30° angle. Find the area of the rhombus.