Geometry Unit 2: Lesson 4, 5, 6, and 7
In the diagram m∠3 = x + 30 and m∠4 = 2x - 80. What is the measure of angle 3?
140
Angles with measures that add to 180°
Supplementary angles
Lesson 5
ANGLE RELATIONSHIP DEFINITIONS
Which of the pairs of angles are complementary?
∠APW and ∠ZPW
Which of the following angles is a right angle?
∠APZ
Given the diagram, a supplement to ∠ABC could be
∠DAB
Given the following diagram, name an obtuse angle.
∠WPB
Two adjacent supplementary angles are
∠ZPB and ∠APZ
Based on the given diagram, if m∠1 = 60°, then m∠2 =
30
Given the following diagram, if m∠COF = 150°, then m∠BOC =
30
In the diagram, m∠COE = 55°. If m∠2 = 2x and m∠3 = x + 10, what is the measure of angle 2?
30
If m∠1 = m∠2, then m∠1 is
45
If m∠APW = 20°, then the measure of ∠WPZ is
70
The theorems in the lesson are followed by which of the following?
A diagram A proof of the theorem
Lesson 6
ANGLE RELATIONSHIP THEOREMS (1)
Lesson 7
ANGLE RELATIONSHIP THEOREMS (2)
1 and 2 are _____.
Adjacent angles
Angles in the same plane with a common vertex and a common side but no common interior points.
Adjacent angles
Conclusion: m∠SPT + m∠TPU = 90° Which of the statements supports the conclusion from the diagram and the GIVEN information.
Adjacent angles whose exterior sides are perpendicular rays are complementary.
Adjacent angles have no common interior points.
Always
Vertical angles are equal in measure.
Always
m∠1 + m∠2 = m∠RST
Angle addition theorem
Vertical angles
Angles with sides that form two pairs of opposite rays.
Angles with measures that add to 90°
Complementary angles
m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90
Definition of complementary
∠RST is a right angle.
Definition of perpendicular lines
m∠RST = 90°
Definition of right angle
Ray ST is perpendicular to Ray SR.
Given
∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.
Given
Complete the reasons for the proof. Given:m ∠3 = m ∠4 To Prove:∠1, ∠2 are supplementary
Given Exterior Opposite Supplementary Angles Equal Substitution Supplementary
Conclusion: RPS is a right angle. Which of the statements supports the conclusion from the diagram and the GIVEN information?
Perpendicular lines meet to form right angles.
Adjacent, right angles are complementary.
Never
Given the following diagram, are and opposite rays?
No
A pair of opposite rays would be ____________.
Ray PA and ray PB
If two angles are both vertical and supplementary, then the angles are _________.
Right
1 and 2 are _____.
Right angles
∠BOD and ∠COA are ________ angles.
Similar
A pair of vertical angles are acute.
Sometimes
If angles are supplementary, then one of the angles is an obtuse angle.
Sometimes
m∠1 + m∠2 = 90°
Substitution
m∠1 + m∠2 = m∠3 + m∠2
Substitution
m∠1 = 90° - m∠2
Subtraction property of equality
m∠1 = m∠3
Subtraction property of equality
Adjacent angles
Two angles in the same plane that have a common vertex and a common side, but no interior points in common.
Supplementary angles
Two angles with measures that, when added together, equal 180°. Each angle is called the supplement of the other.
Complementary angles
Two angles with measures that, when added together, equal 90°. Each angle is called the complement of the other.
∠2 and ∠3 are ________ angles.
Vertical
Angles with sides that form two pairs of opposite rays
Vertical angles
Conclusion: m∠UPW = 90°. Which of the statements supports the conclusion from the diagram and the GIVEN information?
Vertical angles are equal in measure.
Given the following diagram, is ∠1 a supplement of ∠COF?
Yes
Given the following diagram, if m∠1 = m∠4, then all of the following must be complementary angles except.
angles 2 and 3
All of the following must be true statements except __________.
m∠SPT = m∠UPT
