Parallel Lines, Transversals, & Special Angle Pairs

When 2 lines intersect crazy, wonderful things happen!

When 2 lines, rays or segments intersect, 4 angles are created. 1 4 2 3 Angles 1 & 4 are a linear pair = 180° Angles 1 & 2 are a linear pair = 180° Angles 2 & 3 are a linear pair = 180° Angles 3 & 4 are a linear pair = 180° Angles 1 & 3 are VERTICAL ANGLES and are congruent. Angles 4 & 2 are VERTICAL ANGLES and are congruent.

Transversal 2 or more A line, ray, or segment that intersects COPLANAR lines, rays, or segments. Check out the new notation!! The extra set of arrows tell us the lines are parallel. transversal Non-Parallel lines Parallel lines transversal

INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines exterior

Special Angle Relationships Interior Angles <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles <3 & <5 are Same Side Interior angles <4 & <6 are Same Side Interior angles Special Angle Relationships Exterior Angles <1 & <8 are Alternate Exterior angles <2 & <7 are Alternate Exterior angles <1 & <7 are Same Side Exterior angles <2 & <8 are Same Side Exterior angles 1 4 2 6 5 7 8 3 Corresponding Angles Angles that are in the same position on both lines <1 & <5 are Corresponding angles <2 & <6 are Corresponding angles <3 & <7 are Corresponding angles <4 & <8 are Corresponding angles

Let’s Practice Naming Angle Pairs $ Let’s Practice Naming Angle Pairs $ Name a pair of alternate interior angles Name a pair of same side exterior angles Name a pair of same side interior angles Name a pair of alternate exterior angles Name a linear pair Name a pair of vertical angles Name a pair of corresponding angles Name another pair of corresponding angles 1 2 4 3 5 6 7 8

Special Angle Measurement Relationships WHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY Corresponding angles are CONGRUENT 1 4 2 6 5 7 8 3 If the lines are not parallel, these measurement relationships DO NOT EXIST.

What did you discover about angle measures? Let’s look closer Please get: straight edge protractor piece of paper 4. On the same paper, create a pair of non-parallel lines 5. Draw a transversal 6. Using the protractor, measure all the angles Using both sides of the straight edge and a pencil, create a pair of parallel lines Draw a transversal Using the protractor, measure all the angles What did you discover about angle measures?

When lines are parallel, measurement relationships exist. 1 2 4 3 5 6 7 8 1 2 3 4 5 6 8 7 When lines are not parallel, special angle pairs do not have a measurement relationship. Angle pairs always keep the same names regardless if the lines are parallel. When lines are parallel, measurement relationships exist.

Let’s Practice WE DON’T KNOW! m<1=120° 4 2 6 5 7 8 3 Let’s Practice m<1=120° Find all the remaining angle measures AND give the name of the special angle pair. 120° 60° 120° 60° m<1=91° Find all the remaining angle measures AND give the name of the special angle pair. 120° 60° 120° 1 2 4 3 5 6 7 8 60° 89° 91° 91° 89° WE DON’T KNOW!

Vocabulary Parallel lines: Lines that are always equidistant from each other – they will never intersect. (2D or 3D) Perpendicular lines: Lines that intersect at a 90◦ angle. (2D or 3D) Skew lines: Lines that are not parallel but will never intersect. (3D only)

Use the diagram to name each of the following. A pair of parallel planes All lines that are parallel to 3. Four lines that are skew to 4. All lines that are parallel to plane QUV 5. A plane parallel to plane QUW

Identify all pairs of each type of angle in the diagram below right. Corresponding angles Same-side interior angles Alternate interior angles Alternate exterior angles

Angle measures are 103 ◦ and 77◦ Find the value of x and y. Then find the measure of each labeled angle. What kind of angles are these? What is their measurement relationship? How shall we set up the equation? Do it. Angle measures are 103 ◦ and 77◦ x + x – 26 = 180 2x = 206 x = 103 Are we done?

Another practice problem 40° Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 120°

Assignment Practice 3.1 and 3.2