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2.9 warm-up 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=50x b. 6x+2=50 c. 6x+2(x/2)=50 d. 6x+2(2x)=50 10 2.9 warm-up 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=50x b. 6x+2=50 c. 6x+2(x/2)=50 d. 6x+2(2x)=50 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 Theorem – The sum of the measures of the angles of a triangle is 1800. C A + B + C = 1800 A B Pardekooper How does it work ? Combine like terms Substitution • Find the value of x for the following triangle. C like terms Combining 390 0 65 A -sum A + B + C = 1800 substitution 65 + x + 39 = 180 simplify x + 104 = 180 xTriangle + 104 -Angle-Sum 104 = 180 - 104 subtraction x0 x = 76 B simplify subtraction Pardekooper Now, lets look at the different types of triangles. • Equiangular – All angles are congruent Pardekooper Now, lets look at the different types of triangles. • Equilateral – All sides are congruent Pardekooper Now, lets look at the different types of triangles. • Isosceles – Two sides are congruent Pardekooper Now, lets look at the different types of triangles. • Acute – All angles are less than 900 Pardekooper Now, lets look at the different types of triangles. • Right – One angle is 900 Pardekooper Now, lets look at the different types of triangles. • Obtuse – One angle is greater than 900 Pardekooper Now, lets look at the different types of triangles. • 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 Theorem – The measure of each exterior angle of a triangle equals the sum of the measure of its two remote interior angles. C mA = mB + mC A B Pardekooper Lets try a problem. 700 1130 mA = mB + mC 113 = 70 + x 113 - 70 = 70 - 70 + x 43 = x x0 Exterior substitution subtraction simplify Pardekooper