• 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

(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

• 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
• If , then the triangle is a right triangle.
• If , then the triangle is an obtuse triangle.
• c 2  a 2  b 2 If , then the triangle is an acute triangle.

• Find the missing side of the right triangle.

• Find the missing side of the right triangle.

• Find the missing side of the right triangle.

• Find the area of the right triangle.

• Find the area of the right triangle.
53cm

• 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

• Find the remaining two sides of each figure.

• Find the remaining two sides of each figure.
2
3

• Find the remaining two sides of each figure.

• Find the remaining two sides of each figure.
3
3

• 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?

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

• A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden.

• 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