Chapter 3 Parallel and Perpendicular Lines Study Guide

Chapter 3 Parallel and Perpendicular Lines
Study Guide

3.1 Identify Pairs of Lines/Angles
Parallel Lines Parallel Postulate Perpendicular Postulate
Skew Lines Parallel Planes Diagram with a cube/box
Transversals Angles formed by transversals
Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior- (Same Side
Interior) Angles
3.3 Proving Lines Parallel
**Converses used to show lines are PARALLEL
Corresponding Angles Converse Alternate Interior Angles Converse Alternate Exterior Angles Converse Consecutive Interior- (Same Side
Interior) Angles Converse Transitive Property of Parallel Lines
**Don’t Forget About: Linear Pairs- Supplementary
Vertical Angles- Congruent

3.2- Parallel Lines and Transversals
**Know which angles are congruent and supplementary
Corresponding Angles Postulate Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Consecutive Interior- (Same Side
Interior) Angles Theorem
**Know more difficult problems with multiple lines, systems of equations and factoring! (we had 2
worksheets on this!)
3.6 Perpendicular Lines
Theorem 3.8- Two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular
Theorem 3.9- If 2 lines are perpendicular, then they intersect to
form 4 right angles
Right Angle Pair Theorem (3.10)- Two angles that make a right angle pair are
complementary
Perpendicular Transversal Theorem- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
Lines Perpendicular to a Transversal Theorem- If two lines are perpendicular
to the same line, then they are perpendicular to each other

Part I: Circle the word that best completes the sentence. 1. If two lines are parallel, then they (ALWAYS…..SOMETIMES…..NEVER) intersect.

2. If one line is skew to another, then they are (ALWAYS…..SOMETIMES…..NEVER) coplanar.

3. If two lines intersect, then they are (ALWAYS…..SOMETIMES…..NEVER) perpendicular.

4. If two lines are coplanar, then they are (ALWAYS…..SOMETIMES…..NEVER) parallel.

5. If two lines are cut by a transversal such that the alternate interior angles are (CONGRUENT…..COMPLEMENTARY…..SUPPLEMENTARY), then the lines are parallel.

6. If two lines are cut by a transversal such that the consecutive interior angles are (CONGRUENT…..COMPLEMENTARY…..SUPPLEMENTARY), then the lines are parallel.

7. If two lines are cut by a transversal such that the corresponding angles are (CONGRUENT…..COMPLEMENTARY…..SUPPLEMENTARY), then the lines are parallel.

Part II: Think of each segment in the diagram as part of a line. Complete the statement with PARALLEL, SKEW, or PERPENDICULAR.

1. ⃡

⃡ are _______________________

2. ⃡

⃡ are _______________________

3. ⃡

⃡ are _______________________

4.

and

are _______________________

5.

and

are _______________________

Part III: Classify the angle pair as corresponding angles, alternate interior angles, alternate exterior angles, same side (consecutive) interior angles, vertical angles, linear pair, or none.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Part IV: Find the value of the variables. 1.
2.
3.
( (
4.

5.

Part V. Is there enough information to state that lines and are parallel? If so, state the reason.

1.

Yes_________

No__________

Reason (if necessary)____________________________

_______________________________________________

2.

Yes_________

No__________

Reason (if necessary)____________________________

______________________________________________

3.

Yes_________

No__________

Reason (if necessary)____________________________

_______________________________________________

Part VI. Use the diagram and the given information to determine if

, or neither.

1.

_______________

2.

_______________

3.

_______________

4.

_______________

5.

_______________

6.

_______________

7.

_______________

Part VII. Find the measure of the indicated angle.
6 12 5
4 3

1.

_________________

3.

__________________

5.

__________________

2.

_______________________

4.

_______________________

6.

_______________________

Part VIII. Use the diagram.

1. Is r ? Yes__________

2. Is

Yes__________

3. Is r

Yes__________

No___________ No___________ No___________

Part IX. In the diagram, ⃡ 1.
R

⃡ . Find the value of .

S

T

2. R

S

T

3. R

S

T

____________ ____________ ____________

Chapter 3 Review Solutions

Part I: 1) Never 2) Never 3) Sometimes 4) Sometimes 5) Congruent 6) Supplementary 7) Congruent
Part II: 1) Perpendicular 2) Parallel 3) Skew 4) Perpendicular 5) Parallel
Part III: 1) Corresponding angles 2) Alternate exterior angles 3) None 4) Alternate interior angles 5) Vertical angles 6) Consecutive interior angles (same side interior) 7) Alternate exterior angles 8) None 9) Alternate interior angles 10) None 11)Linear Pairs 12)Consecutive Interior

Part VII: 1) 25 2) 52 3) 25 4) 25 5) 65 6) 65
Part VIII: 1) Not enough information 2) Not enough information 3) Yes, both lines perpendicular to m
Part IX: 1) x = 18 2) x = 12 3) x = 15

Part IV: 1) x = 21, y = 25 2) x = 11, y = 25 (system of equations) 3) x = 37, y = 111 4) x = 9, y = 6 (system of equations) 5) x = 84, y = 90, z = 31

Part V: 1) No, the sum of the angles is not 180 degrees 2) No, Corr. Angles are not congruent (one way to show) 3) Yes, alternate exterior angles converse (angles are congruent)

Part VI: 1) m n Alt. Int. Converse 2) Neither-No transversal 3) Neither- Need to be sup. 4) p ll q Consec. Int. Converse

5) p q Alt. Int. Converse 6) m ll n Consec. Int. Converse 7) none- No Transversal