Download Lesson 54: Angle Relationships

Bell Work:
Marsha swam 400 meters in 6
minutes and 12 seconds. Convert
that time to minutes.
Answer:
6.2 minutes
Intersecting lines form pairs of
adjacent angles and pairs of
opposite angles.
Adjacent Angles*: share a
common vertex and a common
side but do not overlap.
Opposite Angles*: are formed by
two intersecting lines and share
the same vertex but do not share a
side.
Opposite angles are also called
vertical angles. Vertical angles are
congruent.
Adjacent Angles:
<1 and <3
<3 and <4
<4 and <2
<2 and <1
Opposite Angles:
<1 and <4
<2 and <3
1
2
3
4
Angles formed by two
intersecting lines are related. If we
know the measure of one of the
angles, then we can find the
measure of the other angles.
Two angles whose measures total
180° are called supplementary
angles. Supplementary angles
may be adjacent angles, but it is
not necessary that they are
adjacent.
Angle pairs formed by two
intersecting lines:
Adjacent angles are
supplementary
Opposite angles (vertical
angles) are congruent
Example:
Refer to this figure to find the
measures of angles 1, 2, 3, and 4.
4
3
2
1
40°
Answer:
<1 = 140°
<2 = 40°
<3 = 50°
<4 = 130°
Two angles whose measures total
90° are complementary angles.
Supplementary = 180°
Complementary = 90°
Transversal*: a line that intersects
one or more other lines in a plane.
If the transversal were
perpendicular to the parallel
lines, then all angles formed
would be right angles.
Corresponding angles: on the
same side of the transversal and
on the same side of each of the
parallel lines. Corresponding
angles of parallel lines are
congruent.
<1 and <5 are corresponding
angles and are thus congruent.
Name 3 more pairs of
corresponding angles.
1
3
5
7
6
8
2
4
Answer:
<3 and <7
<2 and <6
<4 and <8
Alternate Interior Angles: are on
opposite sides of the transversal
and between the parallel lines.
Alternate interior angles of
parallel lines are congruent.
<3 and <6 are alternate interior
angles and thus congruent. Name
another pair of alternate interior
angles.
1
3
5
7
6
8
2
4
Answer:
<4 and <5
Alternate Exterior Angles: are on
opposite sides of the transversal
and outside the parallel lines.
Alternate exterior angles of
parallel lines are congruent.
<1 and <8 are alternate exterior
angles and thus congruent. Name
another pair of alternate exterior
angles.
1
3
5
7
6
8
2
4
Answer:
<2 and <7
Corresponding Angles
Same side of transversal, same side
of lines
Alternate Interior Angles
Opposite sides of transversal,
between lines
Alternate Exterior Angles
Opposite sides of transversal,
outside of lines
In summary, if parallel lines are cut
by a non-perpendicular transversal,
the following relationships exist.
All the obtuse angles that are
formed are congruent
All the acute angles that are formed
are congruent
Any acute angle formed is
supplementary to any obtuse angle
formed
Turn to page 371 in your books.
Begin the practice set problems
(a) – (j)
a) Name two pairs of vertical
angles
Answer:
<a and <c
<b and <d
b) Name four pairs of
supplementary angles
Answer:
<a and <b
<b and <c
<c and <d
<d and <a
c) If m<a is 110 degrees, then
what are the measures of angles b,
c, and d?
Answer:
m<b = 70 degrees
m<c = 110 degrees
m<d = 70 degrees
d) Which angle is the complement
of <g?
Answer:
<f
e) Which angle is the supplement
of <g?
Answer:
<h
f) If m<h is 130 degrees, then what
are the measures of <g and <f?
Answer:
m<g = 50 degrees
m<f = 40 degrees
g) Which angle corresponds to <f?
Answer:
<b
h) Name two pairs of alternate
interior angles.
Answer:
<c and <f
<d and <e
i) Name two pairs of alternate
exterior angles.
Answer:
<a and <h
<b and <g
j) If m<a is 105 degrees, what is
the measure of <f?
Answer:
m<f = 75 degrees
HW: Lesson 54 #1-30