Warm Up- JUSTIFY WHAT THEOREM OR POSTULATE YOU ARE USING!

1) Find the value of x for which a ll t

2) Find the value of y.

3) Find the measurements of the angles.

5070yx

2x

y – 50

y

2x - 75

2x - 20

x +35

Homework Answers

1) Line BE and CG are parallel- converse of corresponding angle postulate

2) Segment CA and segment HR- Converse of corr. Angle post

3) Segment JO is parallel to LM- if two lines and a transversal form SSIA that are supp, then the lines are parallel

4) Segment PQ and segment ST- Converse of Alt. Int. Angle Thm

5) 306) 507) 598) 3110) a//b if two lines and a transversal

form SSIA that are supp, then the lines are //

11) a//b if two lines and a trans. Form SSIA that are suppl, then the two

lines are //12) a//b if two lines and a trans. Form

SSEA that are suppl, then the two lines are //

13) None14) a//b converse of corr angle post15) None16) a//b- Conv of AIAT17) l//m Conv of Corr Angle Post18) a//b if two lines and a trans. Form

AEA that are congruent, then two lines are //

19) a//b Conv of Corr Angle Post20) None21) l//m conv of AIA thm22) a. <1 b. <1 c. <2 d. <3 e.

Converse of Corr Angles

Theorem 3-9: If two lines are parallel to the same line, then they are parallel to each other.

Draw a diagram for this theorem.

Prove the previous theorem.

Given: j // k and r // k Prove: j // r

1

2

3

Perpendicular Line TheoremsDraw a diagram that represents each theorem

Theorem 3-10: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Theorem 3-11: In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180.

m<1 + m<2 + m<3 = 180

Example:Find the value of x, y and z.

1 3

2

y

21

z

39

x65

Draw a triangle that represents each classification.

• Equiangular– All angles are congruent

• Right– One right angle

• Acute– All angles acute

• Obtuse– One obtuse angle

• Equilateral– All sides congruent

• Isosceles– At least two sides congruent

• Scalene – No sides congruent

Vocabulary

1

3 2

Remote Interior Angles

Exterior Angle

Triangle Exterior Angle Theorem • What is the relationship

between the three angles- measure them and draw a conclusion.

1 3

2

m<1 = m<2 + m<3The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Polygon

• Is a closed plane figure with at least three sides that are segments. The sides intersect at their endpoints and no adjacent sides are collinear.• When naming a polygon, start at any vertex and list the

vertices consecutively in a clockwise or counterclockwise direction

Polygon Classification

• Polygons are classified as convex or concave– Convex: has no diagonal with points outside of

the polygon – Concave: has at least one diagonal with points

outside the polygon • Polygons can be classified by the number of

sides it has– Ex. 3 sides- triangle, 4 sides quadrilateral, 5 sides

pentagon

Pairs

The Sum of Polygon Angle Measures

Polygon Number of Sides Number of Triangles Formed

Sum of the Interior Angle Measures

4

5

6

7

8

1. Sketch Polygons with each number of sides. 2. Divide each polygon into triangles by drawing all diagonals that are

possible from one vertex.3. Find the sum of the measures of each polygon using triangle angle sum

theorem.4. Look for patterns in the table, write a rule for the sum of the measures of

the angles of an n-gon.

Polygon Angle Sum Theorem

The sum of the interior angle measure of a convex polygon with n sides is

(n – 2)180°