Chapter 3 Review 3.1: Vocabulary and Notation 3.2: Angles Formed by Parallel Lines and Transversals 3.3: Proving Lines are Parallel 3.4: Theorems about Perpendicular Lines
Name a pair of vertical angles > > 2 and 3 1 and 4 6 and 8 5 and 7
Name a pair of alternate interior angles > > 3 and 7 4 and 8
Name a pair of alternate exterior angles > > 2 and 5 1 and 6
Name a linear pair of angles > > 1 and 2 2 and 4 3 and 4 1 and 3 7 and 8 7 and 6 5 and 6 5 and 8
Name a pair of parallel lines. How do you know they are parallel? Name the transversal > > m n r m || n arrows r
Name a pair of corresponding angles > > 2 and 7 1 and 8 3 and 5 4 and 6
Describe the relationship between the lines using both words and math notation. x y Perpendicular; x y
Describe the relationship between the lines using both words and math notation. x y > > Parallel; x || y
Name a pair of perpendicular segments. P Q R S T U V W
Name a pair of skew segments. P Q R S T U V W Examples:
Name a pair of parallel segments. P Q R S T U V W
Name a pair of parallel planes. P Q R S T U V W
Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation > > m n r Same-side interior angle theorem
Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation > > m n r Corresponding Angles Postulate
Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation > > m n r Linear Pair Theorem
Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation > > m n r Alternate Interior Angles Theorem
Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation > > m n r Alternate Exterior Angles Theorem
If 4 6, why is ? m n r Converse of the Corresponding Angles Theorem
If 3 7, why is ? m n r Converse of the alternate interior angles theorem
If 2 5, why is ? m n r Converse of the alternate exterior angles theorem
If 4 and 7 are supplementary, why is ? m n r Converse of the same-side interior angles theorem
m n r Find the value of x that would guarantee m || n.
m n r
What do you know about x? Why? 10 x x>10: The shortest distance between a point not on a line and the line is the segment perpendicular to the segment.
What do you know about x? Why? 14
Is this a perpendicular bisector? Why or why not? No. We don’t know that the segment has been bisected or the angles formed are right angles– no markings!
Is this a perpendicular bisector? Why or why not? No. You can’t bisect a line– only a segment.
Is this a perpendicular bisector? Why or why not? Yes. The SEGMENT has been cut in half and the figures intersect at 90 °.
Given: h || p Prove: 2 3 StatementsReasons 1. h || p1. Given 2.2. Corresponding angles theorem 3. 1 2 3 4. h p 1 3 Vertical angles theorem Transitive Property of