Unit Three: Angle Relation Theorem (2)

Given the following diagram, if m∠COF = 150°, then m∠BOC = Line AD is perpendicular to line BF 150° 90° 45° 30°

30 degrees

Line AD is perpendicular to line BF Based on the given diagram, if m∠1 = 60°, then m∠2 = 30° 60° 90° 180°

30 degrees

Line RU is perpendicular to Line SW. All of the following must be true statements except: m∠RPS = m∠WPR m∠RPS + m∠SPU = 180 m∠SPT = m∠UPT

Measure of angle SPT = Measure of angle UPT

Given the following diagram, are ray OC and ray OE opposite rays? yes no

No

Given the following diagram, is Angle 1 a supplement of Angle COF? yes no

Yes

m∠RPS = 90° Conclusion: m∠UPW = 90°. Which of the statements supports the conclusion from the diagram and the given information? Vertical angles are equal in measure. Perpendicular lines meet to form right angles. Adjacent angles whose exterior sides are perpendicular rays are complementary. If two angles are complementary to the same angle then they are equal in measure.

Vertical angles are equal in measure.

Match the following reasons with the statements in the given proof. Prove that if two angles are complementary to the same angle then they are equal in measure. 1.∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 3.m∠1 + m∠2 = m∠3 + m∠2 4.m∠1 = m∠3 Given Subtraction property of equality Definition of complementary Substitution

1. Given 2. Definition of complementary 3. Substitution 4. Subtraction property of equality

Match the following reasons with the given statements of the proof. Given: Ray ST is perpendicular to Ray SR To Prove: the measure of angle 1 = 90° - the measure of angle 2 1.Ray ST is perpendicular to Ray SR. 2.∠RST is a right angle. 3. m∠RST = 90° 4. m∠1 + m∠2 = m∠RST 5. m∠1 + m∠2 = 90° 6. m∠1 = 90° - m∠2 Angle addition theorem Definition of right angle Definition of perpendicular lines Subtraction property of equality Given Substitution

1. Given 2. Definition of perpendicular lines 3. Definition of right angle 4. Angle addition theorem 5. Substitution 6. Subtraction property of equality

Line AD is perpendicular to line BF In the diagram, m∠COE = 55°. If m∠2 = 2x and m∠3 = x + 10, what is the measure of angle 2? 15 30 45 60

30

Line AD is perpendicular to line BF If m∠1 = m∠2, then m∠1 is: 30 45 60 90

45

Line RU is perpendicular to Line SW. Conclusion: m∠SPT + m∠TPU = 90° Which of the statements supports the conclusion from the diagram and the given information? Vertical angles are equal in measure. Perpendicular lines meet to form right angles. Adjacent angles whose exterior sides are perpendicular rays are complementary. Adjacent angles whose exterior sides are perpendicular rays are supplementary.

Adjacent angles whose exterior sides are perpendicular rays are complementary.

Given the following diagram, if m∠1 = m∠4, then all of the following must be complementary angles except: Line AD is perpendicular to line BF angles 1 and 2 angles 1 and 3 angles 2 and 3 angles 2 and 4

Angles 2 and 3

Line RU is perpendicular to Line SW. Conclusion: RPS is a right angle. Which of the statements supports the conclusion from the diagram and the given information? Vertical angles are equal in measure. Perpendicular lines meet to form right angles. Adjacent angles whose exterior sides are perpendicular rays are complementary. All right angles are equal in measure.

Perpendicular lines meet to form right angles

Complete the reasons for the proof. Given: the measure of Angle 3 = Measure of Angle 4 To Prove: Angle 1, Angle 2 are supplementary Statement 1. Measure of Angle 3 = Measure of Angle 4 2. Angle 2, Angle 3 are supplementary 3. Measure of Angle 2 + Measure of Angle 3 = 180 degrees 4. Measure of Angle 2 + measure of angle 4 = 180 degrees 5. Measure of angle 1 = measure of angle 4 6. Measure of angle 2 + measure of angle 1 = 180 degrees 7. Angle 1, Angle 2 are supplementary

Reason 1. Given 2. Exterior sides in opposite rays 3. Definition of supplementary angles 4. Substitution 5. Opposite angles are equal 6. Substitution 7. Definition of supplementary angles

Adjacent angles whose exterior sides are opposite rays are ___.

Supplementary