1. Unit 22 TRIANGLES

2. 2 TYPES OF TRIANGLES A polygon is a closed plane figure formed by three or more line segments A triangle is a three-sided polygon The sum of the angles of any triangle is equal to 180° An equilateral triangle has three equal sides. It also has three equal angles

3. 3 TYPES OF TRIANGLES An isosceles triangle has two equal sides.  The equal sides are called legs.  The third side is called the base.  The base angles of an isosceles triangle are equal  The base angles are opposite the legs A scalene triangle has three unequal sides.  It has three unequal angles.

4. 4 TYPES OF TRIANGLES A right triangle has a 90° angle. The symbol for a right angle is a small square placed at the vertex of the angle. The side opposite the right angle is called the hypotenuse. The other two sides are called legs An acute triangle has three acute angles An obtuse triangle has one obtuse angle and two acute angles

5. 5 ISOSCELES AND EQUILATERAL TRIANGLES In an isosceles triangle, an altitude to the base bisects (divides into two equal parts) the base and the vertex angle In an equilateral triangle, an altitude to any side bisects the side and the vertex angle Find sides c and b in the figure below: c 25" 13" b 50° c = 25" (isosceles triangle) b = 26" (13" × 2)

6. 6 PYTHAGOREAN THEOREM The Pythagorean Theorem deals with the relationship of the sides of a right triangle The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs

7. 7 PYTHAGOREAN THEOREM Determine the hypotenuse (c) in the right triangle below: c 5" 7" c 2 = 5 2 + 7 2 c 2 = 74 c = 8.60 Ans Note: The answer is rounded c 2 = 25 + 49

8. 8 PRACTICE PROBLEMS Identify the triangles in problems 1– 3 as scalene, isosceles, or equilateral 1. 4" 2. 20mm 17mm 5mm 3. 20" 15"

9. 9 PRACTICE PROBLEMS (Cont) Define the terms in problems 4–6: 4. Obtuse triangle 5. Right triangle 6. Polygon 7. Given a triangle with  1 = 25 ,  2 = 68 , find  3. 8. Find  A and  B in the triangle below given that  C = 30°. C A B 5"

10. 10 PRACTICE PROBLEMS (Cont) 9. Determine side a in the right triangle shown below. 10. Use the Pythagorean Theorem to find the length of the diagonal in a rectangle with a length of 10 inches and a width of 8 inches. 3.5" 2" a

11. 11 PRACTICE PROBLEMS (Cont) 11. If you know the roof on your house is 40 feet from eve to vertex (peak) and that the width is about 55 feet. How tall is the peak on your house from the ceiling? 12. In the house above if the peak is 86° 15‘48“. What is the angle of the roof to ceiling/trusses on the right side in DMS?

12. 12 PROBLEM ANSWER KEY 1. Equilateral 2. Scalene 3. Isosceles 4. Has one obtuse angle and two acute angles 5. Has a right or 90° angle 6. A closed plane figure formed by three or more line segments 7. 87° 8.  A =  B = 75  9. 2.872 inches (rounded) 10. 12.806 inches (rounded) 11. 29.047 feet 12. 46°52‘6“