When six students and two adults saw a When six students and two adults saw a movie, the total ticket cost was $50. Adult movie, the total ticket cost was $50. Adult tickets cost twice as much as student tickets cost twice as much as student tickets. Which number sentence best tickets. Which number sentence best represents the situation ?represents the situation ?

a. x+2x=50xa. x+2x=50x b. 6x+2=50b. 6x+2=50

c. 6x+2(c. 6x+2(xx//22)=50)=50 d. 6x+2(2x)=50 d. 6x+2(2x)=50

2.9 warm-up

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When six students and two adults saw a When six students and two adults saw a movie, the total ticket cost was $50. Adult movie, the total ticket cost was $50. Adult tickets cost twice as much as student tickets cost twice as much as student tickets. Which number sentence best tickets. Which number sentence best represents the situation ?represents the situation ?

a. x+2x=50xa. x+2x=50x b. 6x+2=50b. 6x+2=50

c. 6x+2(c. 6x+2(xx//22)=50)=50 d. 6x+2(2x)=50 d. 6x+2(2x)=50

2.9 warm-up

10

3.4 Parallel Lines and the Triangle

Angle-Sum theoremYou will be

able to identify the

different types of triangles. You will use

parallel lines to solve for angles in a triangle

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Lets start with a theoremLets start with a theorem

• Triangle Angle-Sum TheoremTriangle Angle-Sum Theorem– The sum of the measures of the angles of The sum of the measures of the angles of

a triangle is 180a triangle is 18000..

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A B

C

A + B + C = 1800

How does it work ?• Find the value of x for the following triangle.Find the value of x for the following triangle.

-sum

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Triangle Angle-Sum

A B

CA + B + C = 1800

650

390

x0

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

Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Equiangular Equiangular – All angles are congruentAll angles are congruent

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Equilateral Equilateral – All sides are congruentAll sides are congruent

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Isosceles Isosceles – Two sides are congruentTwo sides are congruent

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Acute Acute – All angles are less than 90All angles are less than 9000

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Right Right – One angle is 90One angle is 9000

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Obtuse Obtuse – One angle is greater than 90One angle is greater than 9000

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Now, lets look at the different Now, lets look at the different types of triangles.types of triangles.

• Scalene Scalene – No sides are congruentNo sides are congruent

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Here are some terms

Exterior angle of a polygon

Remote interior angles

Just one more theoremJust one more theorem• Triangle Exterior Angle TheoremTriangle Exterior Angle Theorem

– The measure of each exterior angle of a triangle The measure of each exterior angle of a triangle equals the sum of the measure of its two remote equals the sum of the measure of its two remote interior angles.interior angles.

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A B

CmA = mB + mC

Lets try a problem.

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700

1130 x0

mA = mB + mC Exterior

substitution113 = 70 + x subtraction113 - 70 = 70 - 70 + x simplify43 = x