Ch. 6 Geometry

Ch. 6-1 Line and Angle RelationshipsVocabulary for angles:• Acute angles: less than 90°

• Right angles: 90°

• Obtuse angles: more than 90°

• Straight angles: 180 °

Ch. 6-1 Line and Angle RelationshipsVocabulary for angles:• Vertical angles: opposite angles form by

intersecting lines. Vertical angles are congruent.

So,∠1=∠2; ∠3 =∠4• Complementary angles: sum of angles is 90

∠60° +∠30° =∠90°• Supplementary angles: sum of angles is 180

° So,∠120° +∠60° =∠180°

1 23

4

30°60°

60°120 °

Ch. 6-1 Line and Angle Relationships1. Can you tell their

names?

Acute Angle

Vertical Angles

Obtuse Angle

Complementary angles

∠1 ∠3

45°

45°

Ch. 6-1 Line and Angle Relationships1. Can you tell their

names?

Right angles

Straight angles

Supplementary angles

180°

135° 45°

Ch. 6-1 Line and Angle Relationships

2. Find the missing angles

Example 1:

This is a complementary angle. The sum of angles = 90°. So,

x° + 35° = 90°

x = 90° - 35°

x = 55°35°

x°

Ch. 6-1 Line and Angle Relationships2. Find the missing

angles

Example 2:

This is a supplementary angle. The sum of angles = 180°. So,

45° + x° + 55° = 180°

x = 180°- 55° - 45 °

x = 180° - 100 °

x = 80°

55°x°45°

Ch. 6-1 Line and Angle Relationships2. Find the missing

angles

Example 3:

They are a vertical angles. The opposite angles congruent to one another. So,

x° = 75° y° = 105° Reason: vertical

angles

x°75°

105°

y°

Ch. 6-1 Line and Angle Relationships2. Find the missing

angles

Your turn:

x° + 60° = 90°

x = 90° - 60°

x = 30°

60°

x°

Ch. 6-1 Line and Angle Relationships2. Find the missing

angles

Your turn:

x° = 120° y° = 60° Reason: vertical

angles

x°120°

60°

y°

Ch. 6-1 Line and Angle Relationships2. Find the missing

angles

Your turn:

This is a supplementary angle. The sum of angles = 180°. So,

80° + x° + 35° = 180°

x = 180°- 80° - 35 °

x = 65°

35°x°80°

Ch. 6-1 Line and Angle RelationshipsVocabulary for lines:• Perpendicular Lines: Lines intercept at right

angles. Symbol: e.g. m n

• Parallel Lines: Lines never intersect or cross. Symbol: II

• Transversal: A line that intersects 2 or more lines.

Right angle symbol indicates the lines are perpendicular.

The arrowheads indicate that two lines are parallel.

Ch. 6-1 Line and Angle RelationshipsVocabulary for lines:What happen when a transversal passes through two parallel lines?

1. Alternate Interior Angles are congruentSo, x°= y°

2. Alternate Exterior Angles are congruent So, a°= b°

3. Corresponding angles are congruent. So, s°= t °

x°

y°

a°

b°

s °t °

Ch. 6-1 Line and Angle Relationships3. Find the angle measureExample 1 (2001 FCAT):

Tyrone is building a picnic tableto be used in a local park. An end view of the picnic table is shownbelow. Tyrone needs to know themeasure of angle x. The top ofthe table will be parallel to theground. One side of each leg willmeet the ground at a 145° angle.What is the measure, in degrees,of angle x?

A. 35 ° B. 45 ° C. 145 ° D. 180 °

Angle x ° and angle 145 ° are alternate interior angles. They are congruent. So, x ° = 145 °

C is the answer

145°

x°

Ch. 6-1 Line and Angle Relationships3. Find the angle

measure

Your turn:

1. Find 2 if 1 = 63°∠ ∠2. Find 3 if 8 = 100°∠ ∠3. Find 4 if 7 = 82°∠ ∠

1. Find 2 if 1 = 63°∠ ∠∠2 and 1 are∠corresponding angles. Their angles are congruent. So, 2 = 1 = 63 °. ∠ ∠

2. Find 3 if 8 = 100°∠ ∠∠3 and 8 are alternate exterior ∠angles. Their angles are congruent. So, 3 = 8 = 100°∠ ∠

3. Find 4 if 7 = 82°∠ ∠∠4 and 7 are supplementary ∠angles. The sum of their angles equal to 180°, So, 4 + 7 = 180°∠ ∠ ∠4 + 82° = 180°

∠4 = 180° – 82° ∠4 = 98°

1 2

3

8

76

5

4