do now draw each figure. 1. line segment 2. line 3. ray 4. plane course 2 8-3 eq : how do i identify...
TRANSCRIPT
Do NowDraw each figure.
1. line segment
2. line
3. ray
4. plane
Course 2
8-3EQ: How do I identify parallel, perpendicular, and angles formed by a transversal?
HWK: Wbk P 70
• M7A2a Given a problem, define a variable, write an equation, solve the equation and interpret the solution.
Vocabulary ReviewAngle – Vertex - right angle - angle that that measures.
The symbol Γ indicates a right angle.
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Course 2
Angles
acute angle - is an angle that measures
obtuse angle - an angle that measures
straight angle - is an angle that measures
complementary angles – the sum of the measures of two angles is ?0
supplementary angles – the sum of the measures of two angles is ?°
perpendicular lines - angles formed by two
intersecting lines are equal to 90°
parallel lines - lines in the same plane do
not intersect at all
adjacent angles – angles that have a
common vertex and a common side, but
no common interior points.
vertical angles - opposite angles formed
by two intersecting lines
Transversal - a line that intersects two or
more lines
corresponding angles - are angles on the
same side of the transversal and are
both above or both below the parallel
lines
An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.
Angles are measured in degrees (°).
A
CB
1
Vertex
Course 2
8-3 Angles
An angle’s measure determines the type of angle it is.
A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.
An obtuse angle is an anglethat measures more than 90°but less than180°.
A straight angle is an anglethat measures 180°.
Course 2
8-3 Angles
Tell whether each angle is acute, right, obtuse or straight.
Additional Example 1: Classifying Angles
A. B.
obtuse angle acute angle
Course 2
8-3 Angles
Check It Out: Example 1
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Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
Course 2
8-3 Angles
If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.
Course 2
8-3 Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
OMP and PMQ
complementary.
O
N
P Q
R
M
Course 2
8-3 Angles
If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°.
Reading Math
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
NMO and OMR
O
N
P Q
R
M
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
PMQ and QMR
O
N
P Q
R
M
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
BAC and CAF
C
B
D
E
F
A
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
CAD and EAF
C
B
D
E
F
A
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-3 Angles
BAC and EAF
C
B
D
E
F
A
Angles A and B are complementary. If mA is 56°, what is the mB? What is the supplement of A?
Course 2
8-3 Angles
Angles P and Q are supplementary. If mP is 32°, what is the mQ? What is the complement of P?
Course 2
8-3 Angles
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel or perpendicular.
The lines appear to intersect to form right angles.
UV and YV
UV YV
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel or perpendicular.
The lines are in the same plane and do not intersect.
XY and WZ
XY || WZ
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel or perpendicular.
The lines appear to intersect to form right angles.
WX and XU
WX XU
Course 2
8-3 Angle Relationships
Tell whether the lines appear parallel or perpendicular.
The lines are in the same plane and do not intersect.
WX and ZY
WX || ZY
Course 2
8-3 Angle Relationships
Course 2
8-3 Angle Relationships
Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary
Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
Course 2
8-3 Angle Relationships
A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.
Course 2
8-3 Angle Relationships
Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.
Line n line p. Find the measure of the angles.
45°
2 3 135°
5 647
n p
Course 2
8-3 Angle Relationships
Tell whether each angle is acute, right, obtuse, or straight.
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1. straight
obtuse
Course 2
8-3 Angles TOTD
2.
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
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3. AZB and BZC neither
Course 2
8-3 Angles TOTD
4. BZC and CZD complementary
5. Angles M and N are supplementary. If M is 117°, what is mN? 63°