Download 8-3 Angle Relationships

8-3 Angle Relationships
Warm Up
Complete each sentence.
!
1. Angles whose measures have a sum of 90° are
_______________ .
!
2. A part of a line that starts at one point and extends
forever in one direction is called a _______.
!
3. Angles whose measures have a sum of 180° are
______________.
!
4. A part of a line between two points is called a
____________.
Holt CA Course 1
8-3 Angle Relationships
Additional Example 1: Finding Angle Measures
Use the diagram to find each angle
measure.
A. If m∠1 = 37°, find m∠ 3.
∠1 and ∠2 are supplementary.
m∠2 = 180° – 37° = 143°
The measures of ∠2 and ∠3 are supplementary.
m∠3 = 180° – 143° = 37°
So m∠1 = m∠3, or ∠1 ≅ ∠3.
Holt CA Course 1
8-3 Angle Relationships
Writing Math
~ which is read as
The symbol for congruence is =,
“is congruent to.”
Holt CA Course 1
8-3 Angle Relationships
Additional Example 1: Finding Angle Measures
Use the diagram to find each angle measure.
B. If m∠4 = y°, find m∠2.
∠3 and ∠4 are supplementary.
m∠3 = 180° – y°
∠2 and ∠3 are supplementary.
m∠2 = 180° – m∠3
o – yo for
Substitute
180
= 180° – (180o – yo) m∠3.
= 180° – 180° + y° Distributive Property
= y°
Simplify.
So m∠4 = m∠2, or ∠4 ≅ ∠2.
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 1
Use the diagram to find each angle measure.
2
A. If m∠1 = 42°, find m∠3.
Holt CA Course 1
1
3
4
8-3 Angle Relationships
Check It Out! Example 1
Use the diagram to find each angle measure.
B. If m∠4 = x°, find m∠2.
2
1
Holt CA Course 1
3
4
8-3 Angle Relationships
The angles in Example 1 are examples of
adjacent angles and vertical angles. These
angles have special relationships because
of their positions.
Adjacent angles have a common vertex
and a common side, but no common
interior points.
Vertical angles are the nonadjacent
angles formed by two intersecting lines.
Holt CA Course 1
8-3 Angle Relationships
A transversal is a line that intersects two
or more lines that lie in the same plane.
Transversals to parallel lines form angle
pairs with special properties.
Holt CA Course 1
8-3 Angle Relationships
Holt CA Course 1
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
l
|| line m. Find the measure
of the angle.
A. ∠4
Corresponding angles are congruent.
m∠4 = 124°
Holt CA Course 1
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
l
|| line m. Find the measure
of the angle.
B. ∠2
∠2 is supplementary to the 124° angle.
m∠2 + 124° = 180°
–124°
m∠2
Holt CA Course 1
–124° Subtract.
= 56° Simplify.
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
l
|| line m. Find the measure
of the angle.
∠2 and ∠6 are corresponding angles.
C. ∠6
m∠6 = 56°
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
l
|| line m. Find the measure
of the angle.
Alternate exterior angles are congruent.
A. ∠7
1
Holt CA Course 1
144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
l
|| line m. Find the measure
of the angle.
B. ∠1
1
Holt CA Course 1
144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
l
|| line m. Find the measure
of the angle.
C. ∠6
1
Holt CA Course 1
144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Lesson Quiz
In the figure, line a || line b.
1. Name all angles congruent to ∠3.
2. Name all the angles supplementary to ∠6.
3. If m∠1 = 105° what is m∠3?
4. If m∠5 = 120° what is m∠2?
Holt CA Course 1