Bell Work 1) 2) 3) Write the conditional as it’s converse, inverse, and contrapositive If it is warm outside, then it is sunny. 4) Evaluate this biconditional statement. (Hint: you need to write the conditional and the converse.) Two angles add to 90°, if and only if they are supplementary.

Outcomes I will be able to: 1) Identify the relationship between 2 lines or planes 2) Name pairs of angles formed by lines and a transversal 3) Use properties of parallel lines to determine congruent angles

Lines Parallel Lines: Lines that are coplanar and do not intersect Ex: and Skew Lines: Lines that are not coplanar and do not intersect Ex: and Parallel Planes: Planes that do not intersect Ex: Plane u and Plane w

Example 1 1. Find examples of parallel lines, skew lines and parallel lines in the picture. Parallel Lines: Line AB and Line CD; Line AE and Line DH Line BF and Line CG; Line EH and AD Skew Lines: Line AB and Line DH; Line CD and EF Line FG and AE; Line EH and BC Parallel Planes: Plane ABCD and Plane EFGH; Plane ADHE and Plane BCGF Plane DCGH and Plane ABFE

More Angle Relationships Transversal: A line that intersects two or more coplanar lines at different points. The angles formed by the two lines and a transversal are given special names. Which line is the transversal? Line t Corresponding Angles: Angles that are located on the same side of the transversal and in the same relative location(ie. both on top or both on bottom) Ex:

More Angle Relationships Alternate Exterior Angles: Angles that lie outside the two lines and are on opposite sides of the transversal. Ex: Alternate Interior Angles: Angles that lie between the two lines and are on opposite sides of the transversal. Ex: Same Side Interior Angles: Angles that lie between the two lines and are on the same side of the transversal Ex:

Parallel Lines Investigation Follow the instructions on the Guided Investigation 3.3 in the text book. Create a set of parallel lines using the opposite edges of the ruler to form them Answer all of the questions What do you notice about corresponding angles, alternate interior angles, and alternate exterior angles in parallel lines?

Angles in Parallel Lines Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then corresponding angles are congruent. Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then same side interior angles are supplementary

Angles in Parallel Lines Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. Examples: 1) Use the properties of parallel lines to find the value of x. How can we solve this? See board for work

Examples 2) Find the values of x and y in the diagram. What type of angles are (2y + 7) and 109? What do we know about them b/c of that? 2y + 7 = 109 What do we know about 109 and x? x = 180

Examples 3) Find the values of x and y in the diagram. What do we know about 7(x – 19) and 84? They are Alternate Exterior, so: 7(x – 19) = 84 What do we know about 7(x – 19) and (3y +6)? 7(x – 19) + 3y + 6 = 180

Independent Practice Complete the 12 problems on the back of your notes