CHAPTER 3CHAPTERREVIEW

Relationships Between Lines:

GOAL: Identify relationships between lines

Two lines are parallel lines if they lie in the same plane and do not intersect.

Two lines are perpendicular lines if they intersect to form a right angle.

p

q

n

m

Two lines are skew lines if they do not lie in the same plane.Skew Lines never intersect.

●

c

b

A

X

W

V

U

T

S

R

QName a line that is skew to VW.

Name a plane that appearsparallel to plane VWX.

Name a line that is perpendicular to plane VWX.

All segments in the diagramare part of a line and all corners of the cube form right angles.

THEOREMS ABOUT PERPENDICULAR LINES:

GOAL: Use theorems about perpendicular lines

Theorem 3.1

Words: All right angles are congruent.

Symbols: If the m A = 90° and m B = 90°,then A B

A

B

Theorem 3.2

Words: If two lines are perpendicular, thenthey intersect to form four right angles.

Symbols: If n m, then m 1 = 90°, m 2 = 90°,m 3 = 90°, and m 4 = 90°.

43

1

2

Theorem 3.3

Words: If two lines intersect to form adjacent congruent angles, thenthe lines are perpendicular.

Symbols: If 1 2, then AC BD ●D

●B

●C

A1

2

Theorem 3.4

Words: If two sides of adjacent acute anglesare perpendicular, then the angles are complementary.

Symbols: If EF EH, then m 3 + m 4 = 90° ●H

● G

F ●

●E

34

In the diagram at the right,EF EH and m GEH = 30 °.Find the value of y.

30°

2y – 12

F ●

E ●●G

●H

12

34

5

67

8

1. Name a pair of alternate interior angles

2. Name a pair of corresponding angles.

3. Name a pair of same-side interior angles.

4. Name a pair of alternate exterior angles.

72° 1

2 3

4 5

6 7

If j ǁ k then find:

1. m<12. m<23. m<34. m<45. m<56. m<67. m<7

≫

≫j

k

120°

2x + 32

Solve for x.

≫

≫

3x – 15

45°

Solve for x.

≫

≫

74°

5x + 14

Solve for x.

≫

≫

103°

6y – 23

Solve for y.

≫

≫

Showing Lines are Parallel

Goal: Show that two lines are parallel.

The converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion.

Write the converse for the given if-then statement:

1. If two angles have the same measure, then the two angles are congruent.

Examples:

Determine the postulate that proves the lines are parallel.

1.63°

63°

2.55°

125°

3.

138°

138°

56°

56°

145°

145°5.

4.

Theorem 3.11

Words: If two lines are parallel to the same line, then they are parallel to each other.

Symbols: If q ǁ r and r ǁ s, then q ǁ s.

s

q

r

Theorem 3.12

Words: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Symbols: If m p and n p then m ǁ n.

p

m n

Determine whether if the given picture is a translation.

1. 2.

3. 4.

PRACTICEPAGE 160-163

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