Podcast
Questions and Answers
What theorem justifies the statement that ∠2 ≅ ∠3 in the second proof?
What theorem justifies the statement that ∠2 ≅ ∠3 in the second proof?
- Vertical angles theorem (correct)
- Complement theorem
- Triangle similarity theorem
- Transitive property of equality
Which property is used when concluding that 5x = 80 in the second proof?
Which property is used when concluding that 5x = 80 in the second proof?
- Subtraction property of equality
- Multiplication property of equality
- Addition property of equality (correct)
- Simplification property
What is the value of m∠1 in the third proof if x = 9?
What is the value of m∠1 in the third proof if x = 9?
- 135°
- 180°
- 144° (correct)
- 54°
Which step employs the transitive property in the first proof?
Which step employs the transitive property in the first proof?
What conclusion can be drawn from m∠QRS = 75° and the angle addition postulate in the second proof?
What conclusion can be drawn from m∠QRS = 75° and the angle addition postulate in the second proof?
Flashcards
Vertical Angles Theorem
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
Angle Addition Postulate
Angle Addition Postulate
If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC.
Linear Pair
Linear Pair
Two adjacent angles that form a straight line.
Supplementary Angles
Supplementary Angles
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Congruent Angles
Congruent Angles
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Study Notes
Angle Proofs - Practice Problems
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Problem 1: Given ∠1 ≅ ∠2 and m∠1 = m∠3, prove m∠1 = m∠3.
- Statements: 1. ∠1 ≅ ∠2, 2. ∠2 ≅ ∠3, 3. ∠1 ≅ ∠3, 4. m∠1 = m∠3
- Reasons: 1. Given, 2. Given, 3. Transitive Property of Congruence, 4. Definition of Congruent Angles
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Problem 2: Given T is in the interior of ∠QRS, m∠QRS = 75°, m∠QRT = (3x - 1)°, and m∠TRS = (2x - 4)°, find x.
- Statements: 1. T is in the interior of ∠QRS, 2. m∠QRT + m∠TRS = m∠QRS, 3. m∠QRS = 75°, 4. m∠QRT = (3x - 1)°, 5. m∠TRS = (2x - 4)°, 6. (3x - 1) + (2x - 4) = 75, 7. 5x - 5 = 75, 8. 5x = 80, 9. x = 16
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Problem 3: Given ∠1 and ∠2 form a linear pair, m∠1 = (15x + 9)°, and m∠2 = (4x)°, find x.
- Statements: 1. ∠1 and ∠2 form a linear pair, 2. ∠1 and ∠2 are supplementary, 3. m∠1 + m∠2 = 180°, 4. m∠1 = (15x + 9)°, 5. m∠2 = (4x)°, 6. (15x + 9) + (4x) = 180°, 7. 19x + 9 = 180, 8. 19x = 171, 9. x = 9
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