Parallel Lines & Angles EQ: How do I know when to set angles equal to each other or add them and set them equal to 180? NC.M2.G-CO.9 Prove theorems about lines and angles and use them to prove relationships in geometric figures including: Vertical angles are congruent. When a transversal crosses parallel lines, alternate interior angles are congruent. When a transversal crosses parallel lines, corresponding angles are congruent. Points are on a perpendicular bisector of a line segment if and only if they are equidistant from the endpoints of the segment. Use congruent triangles to justify why the bisector of an angle is equidistant from the sides of the angle. NC.M2.G-CO.10 Prove theorems about triangles and use them to prove relationships in geometric figures including: The sum of the measures of the interior angles of a triangle is 180º. An exterior angle of a triangle is equal to the sum of its remote interior angles. The base angles of an isosceles triangle are congruent. The segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length.

Practice Problem = 2 minutes – GO! 1 3 4 6 5 7 8 The m < 1 is 45 degrees, find the remaining angles.

How did you do? 2 = 135 1 = 45 3 = 45 4 = 135 6 = 135 5 = 45 7 = 45 8 = 135 The m < 1 is 45 degrees, find the remaining angles.

Make sure you know the following Vocabulary

Vocabulary Angle: Angles are created by two distinct rays that share a common endpoint (also known as a vertex). ∠ABC or ∠B denote angles with vertex B. Adjacent Angles: Angles in the same plane that have a common vertex and a common side, but no common interior points. Alternate Exterior Angles : Alternate exterior angles are pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on opposite sides of the transversal and are outside the other two lines. When the two other lines are parallel, the alternate exterior angles are equal. Alternate Interior Angles: Alternate interior angles are pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on opposite sides of the transversal and are in between the other two lines. When the two other lines are parallel, the alternate interior angles are equal.

Complementary Angles: Two angles whose sum is 90 degrees. Vocabulary Complementary Angles: Two angles whose sum is 90 degrees. Linear Pair: Adjacent, supplementary angles. Excluding their common side, a linear pair forms a straight line. Supplementary Angles: Two angles whose sum is 180 degrees. Transversal: A line that crosses two or more lines. Vertical Angles: Two nonadjacent angles formed by intersecting lines or segments. Also called opposite angles.

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 2 are called SUPLEMENTARY ANGLES They are a linear pair. ALL linear pairs are supplementary (their measures add up to 180̊ ). Name other supplementary pairs with your Seatmate Partner:

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 3 are called VERTICAL ANGLES They are congruent m<1 = m<3 Name other vertical pairs with your Seatmate Partner:

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 5 are called CORRESPONDING ANGLES They are congruent m<1 = m<5 Corresponding angles occupy the same position on the top and bottom parallel lines. Name other corresponding pairs:

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 4 and < 6 are called ALTERNATE INTERIOR ANGLES They are congruent m<4 = m<6 Alternate Interior on the inside of the two parallel lines and on opposite sides of the transversal. Name other alternate interior angles.

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 4 and < 6 are called ALTERNATE EXTERIOR ANGLES They are congruent m<2 = m<8 Alternate Interior on the inside of the two parallel lines and on opposite sides of the transversal. Name other alternate exterior angles.

Practice Problems = 2 minutes – GO! 1 3 4 6 5 7 8 The m < 6 is 125 degrees, Find the rest of the angles.

How did you do? 2 = 70 1= 110 3 = 110 4 = 70 6 = 70 5 = 110 7 = 110 8 = 70 The m < 6 is 70 degrees, Find the rest of the angles.

This is the Math 2 Level!!! 2x + 20 x + 10 What do you know about the angles? Write the equation. Solve for x. SUPPLEMENTARY 2x + 20 + x + 10 = 180 3x + 30 = 180 3x = 150 x = 30

Yippy – Math 2 Level! 3x - 120 2x - 60 What do you know about the angles? Write the equation. Solve for x. ALTERNATE INTERIOR 3x - 120 = 2x - 60 x = 60 Subtract 2x from both sides Add 120 to both sides