2. When six students and two adults saw a movie, the total ticket cost was $50. Adult tickets cost twice as much as student tickets. Which number sentence best represents the situation ? a. x+2x=50xb. 6x+2=50 c. 6x+2( x / 2 )=50d. 6x+2(2x)=50 2.9 warm-up 10

3. When six students and two adults saw a movie, the total ticket cost was $50. Adult tickets cost twice as much as student tickets. Which number sentence best represents the situation ? a. x+2x=50xb. 6x+2=50 c. 6x+2( x / 2 )=50d. 6x+2(2x)=50 2.9 warm-up 10

4. 3.4 Parallel Lines and the Triangle Angle-Sum theorem You will be able to identify the different types of triangles. You will use parallel lines to solve for angles in a triangle Pardekooper

5. Lets start with a theorem Triangle Angle-Sum TheoremTriangle Angle-Sum Theorem –The sum of the measures of the angles of a triangle is 180 0. Pardekooper AB C  A +  B +  C = 180 0

6. How does it work ? Find the value of x for the following triangle.   -sum Pardekooper Triangle Angle-Sum A B C  A +  B +  C = 180 0 65 0 39 0 x 0 Substitution 65 + x + 39 = 180 substitution Combining like terms x + 104 = 180 simplify subtraction x + 104 - 104 = 180 - 104 subtraction Combine like terms x = 76 simplify

7. Now, lets look at the different types of triangles. Equiangular Equiangular  –All angles are congruent Pardekooper

8. Now, lets look at the different types of triangles. Equilateral Equilateral  –All sides are congruent Pardekooper

9. Now, lets look at the different types of triangles. Isosceles Isosceles  –Two sides are congruent Pardekooper

10. Now, lets look at the different types of triangles. Acute Acute  –All angles are less than 90 0 Pardekooper

11. Now, lets look at the different types of triangles. Right Right  –One angle is 90 0 Pardekooper

12. Now, lets look at the different types of triangles. Obtuse Obtuse  –One angle is greater than 90 0 Pardekooper

13. Now, lets look at the different types of triangles. Scalene Scalene  –No sides are congruent Pardekooper

14. Here are some terms Exterior angle of a polygon Remote interior angles

15. Just one more theorem Triangle Exterior Angle TheoremTriangle Exterior Angle Theorem –The measure of each exterior angle of a triangle equals the sum of the measure of its two remote interior angles. Pardekooper A B C m  A = m  B + m  C

16. Lets try a problem. Pardekooper 70 0 113 0 x 0 m  A = m  B + m  C  Exterior  substitution 113 = 70 + x subtraction 113 - 70 = 70 - 70 + x simplify 43 = x