Transcript Document 344484

Lesson 6-1
Line and Angle Relationships
Definitions
• Acute Angles – Angles with measures less than
90°.
• Right Angles - Angles with a measure of 90.
• Obtuse Angles - Angles with measures between
90° and 180°.
• Straight Angles – Angles with measures equal to
180.
• Vertical Angles are opposite angles formed
by intersecting lines. They are congruent.
• Adjacent Angles have the same vertex,
share a common side, and do not overlap.
• The sum of the measures of complementary
angles is 90°.
• The sum of the measures of supplementary
angles is 180°
Examples 1 and 2
Classify each angle or angle pair using all names that
apply.
m ∠1 is greater than
1
90°. So, ∠1 is an
Ex. 1
obtuse angle.
Ex. 2
1
2
∠1 and ∠2 are adjacent
angles since they have
the same vertex, share
a common side, and do
not overlap.
Together they form a straight angle measuring 180°.
So, ∠1 and ∠2 are also supplementary angles.
Classify each angle or angle pair using all names that apply.
a.
b.
30°
60°
c.
3
4
Example 3
In the figure m∠ABC = 90°. Find the value of x.
A
B
x°
65
°
m∠ABD + m∠DBC = 90°
x + 65 = 90
- 65= -65
x = 25
D
C
Find the value of x in each figure.
d.
x
°
e.
38°
x°
150
°
Definitions
• Lines that intersect at right angles are called
perpendicular lines.
• Two lines in a plane that never intersect or cross
are called parallel lines.
p
m
n
Symbol:
m⟘n
Symbol:
p q
q
Definitions
• A line that intersects two or more other lines is
called a transversal. When a transversal intersects
two lines, eight angles are formed that have
special names.
• If two lines cut by a transversal are parallel, then
these special pairs of angles are congruent.
1
2
4
3
5
8
6
7
transversal
Definitions
• Alernate Inerior Angles – Those on
opposite sides of the transversal and
inside the other two lines are congruent.
Ex. ∠2 ≅ ∠8
• Alternate Exterior Angles – Those on
opposite sides of the transversal and
outside the other two lines, are
congruent.
Ex. ∠4 ≅ ∠6
• Corresponding Angles - Those in the
same position on the two lines in relation
to the transversal, are congruent.
Ex. ∠3 ≅ ∠7
1
2
4
3
5
6
8
7
Example 4
You are building a bench for a picnic table. The top of
the bench will be parallel to the ground. If m∠1 =
148°, find m∠2 and m∠3.
3
1
2
Since ∠1 and ∠2 are
alternate interior
angles, they are
congruent. So, m∠2 =
148°.
Since ∠2 and ∠3 are supplementary, the sum of their
measures is 180°. Therefore, m∠3 = 180° - 148° or
32°.