Ch. 10 Geometry: Line and Angle Relationships. Vocabulary for angles: Acute angles: less than 90°...
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Transcript of Ch. 10 Geometry: Line and Angle Relationships. Vocabulary for angles: Acute angles: less than 90°...
Ch. 10 Geometry:Line and Angle Relationships
Vocabulary for angles:• Acute angles: less than 90°
• Right angles: 90°
• Obtuse angles: more than 90°
• Straight angles: 180 °
Vocabulary 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 °
Line and Angle Relationships
1. Can you tell their names?
Acute Angle
Vertical Angles
Obtuse Angle
Complementary angles
∠1 ∠3
45°
45°
Line and Angle Relationships
1. Can you tell their names?
Right angles
Straight angles
Supplementary angles
180°
135° 45°
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°
Line and Angle Relationships
2. 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°
Line and Angle Relationships
2. 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°
Line and Angle Relationships
2. Find the missing angles
Your turn:
x° + 60° = 90°
x = 90° - 60°
x = 30°
60°
x°
Line and Angle Relationships
2. 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°
Vocabulary 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.
Vocabulary 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 °
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°
Line and Angle Relationships
3. 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°
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3
8
76
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