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)= warm-up 10

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)= warm-up 10

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

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

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

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

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

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

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

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

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

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

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

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

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