1. PSAT MATHEMATICS 9-J Triangles G EOMETRY 1

2. Angles of a Triangle In any triangle, the sum of the measures of the three angles is _______. 2

3. Example In the figure, what is the value of x? 3

4. _____________ Angle AAn ___________ angle of a triangle is an angle formed by one side of the triangle and the extension of another side. TThe measure of an ____________ angle of a triangle is _______ to the sum of the measures of _______________________________________. 4

5. Example In the figure, what is the value of w? 5

6. In any triangle… TThe ____________ side is opposite the ____________ angle. TThe ____________ side is opposite the ____________ angle. SSides with the ________ length are opposite angles with the ________ measure. 6

7. Types of Triangles  Isosceles  Equilateral 7

8. Example Which of the following statements about triangle ABC in the figure must be true? I. m A = 70° II. BC = 10 III. Perimeter of ABC = 30 A.) I only B.) II only C.) I and II only D.) I and III only E.) I, II, and III 8

9. Right Triangles  Angles  Hypotenuse  Legs 9

10. Example In the figure, what is the average (arithmetic mean) of x and y? 10

11. Pythagorean Theorem 11

12. Example Which of the following are not the sides of a right triangle? A. 6, 8, 10 B. 1, 1, √2 C. 1, √3, 2 D. √3, √4, √5 E. 5, 12, 13 12

13. Dividing shapes…  A diagonal of a square divides the square into two _____________________.  An ___________ of a triangle is a line segment drawn from a vertex, _______________ to the opposite side.  An ___________ divides an equilateral triangle into two ____________________. 13

14. Example What is the area of a square whose diagonal is 4? A. 4 B. 8 C. 16 D. 4√3 E. 16√3 14

15. Example In equilateral triangle ABC, the length of the altitude AD is 6. What is the perimeter of ABC? A. 18 B. 6√3 C. 12√3 D. 18√3 E. 36 15

16. Triangle Inequality  The __________ of the lengths of any two sides of a triangle is ____________ than the length of the third side. 16

17. Example If the lengths of two of the sides of a triangle are 7 and 8, which of the following could be the length of the third side? I. 1 II. 2 III. 15 A. None B. I only C. II only D. I and II only E. I, II, and III 17

18. Area of a Triangle 18

19. Example What is the area of an equilateral triangle whose sides are 10? A. 30 B. 25√3 C. 50 D. 50√3 E. 100 19

20. Practice Problems 20