2. Triangles; Objective: To find the perimeter and area of a triangle.

3. Triangles A 3-sided figure named by the three points endpoints are called vertices of the triangle A B C

4. Equilateral Right Scalene Isosceles All sides equal Two sides equal No sides equalHas a 90 o angle; special properties TRIANGLES

5. Definition Notes about Right Triangles –The sides of the triangle that create the right angle are called the legs –The side of the triangle that is opposite the right angle is called the hypotenuse hypotenuse leg

6. Definition Notes about Isosceles Triangles –The congruent sides of the triangle are called the legs –The third side of the triangle is called the base leg base

7. Equilateral Right Scalene Isosceles TRIANGLES

8. EXAMPLE #1 FIND THE PERIMETER P = 4 + 6 + 8 P = 18 cm P = s 1 + s 2 + s 3

9. The perimeter of the triangle is 16 in. A) What is x? B) What are the side lengths? 16 = 3x - 2 18 = 3x 6 = x 2) 6 in, 6 in, 4 in EXAMPLE #2 16 = x + x + (x – 2) A) P = s 1 + s 2 + s 3

10. PRACTICE #1 1. Find the perimeter of the triangle. 6 ft 8 ft 10 ft 2. Find the length of the hypotenuse if the perimeter is 12 inches. X + 1 x X + 2

11. Area of a Triangle The formula for the area of a triangle is b = base h = height h b Notice the base and the height form the 90 ⁰ angle

12. Height/Altitude h h h Height is also called an altitude Altitude: a line segment that connects a vertex to the base forming a 90 ⁰ angle.

13. Where does the area formula come from? Length = Base Width = Height Area Rectangle = l x w

14. Length = Base Width = Height What shapes do you see? How much area does one triangle make-up of the rectangle? ½ Two triangles

15. 8 12 6 9 EXAMPLE #3 Find the area of the triangle

16. x + 1 x The area of the triangle above is 15 cm 2. 1)What is the height? 2)What is the base? x = -6 x = 5 Base = 5 cm Height = 6 cm EXAMPLE #4

17. 10 ft 6 ft What is the area of the unshaded region? Unshaded region = Area of rectangle – 2( Area of triangle) = 60 ft 2 Area of triangles = 2 ( ½ bh ) = 2( EXAMPLE #5 Area of rect. = (l x w ) = (20)(6) = 120 ½)(6)(10) = 60 Area of unshaded = 120 – 60

18. Pythagorean Theorem b a c The Pythagorean Theorem is only used with a right triangle. c represents the hypotenuse. a and b are the legs of the triangle

19. x 12 mm 15 mm Find the area. EXAMPLE #6 First find the missing side length A = (9)(12) = 54 mm ² ½

20. PRACTICE #2 1. The length of the base of a triangle is 3 cm and the height is 2 cm. What is the area of the triangle? 2. Find the area of the shaded region. 3.6 in. 4 in.

21. http://www.youtube.com/watch?gl=GB&hl=en- GB&v=o2Z6tDSb6c8&feature=related Triangle song – sesame street