Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. Justify the statement with a property of equality or a

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1 Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the Angle Addition Postulate Theorems 2.3 and 2.4 Example 2: Real-World Example: Use Supplement or Complement Theorem 2.5: Properties of Angle Congruence Proof: Symmetric Property of Congruence Theorems 2.6 and 2.7 Proof: One Case of the Congruent Supplements Theorem Example 3: Proofs Using Congruent Comp. or Suppl. Theorems Theorem 2.8: Vertical Angles Theorem Example 4: Use Vertical Angles Theorems : Right Angle Theorems 1

2 Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. Justify the statement with a property of equality or a property of congruence. Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI. State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate. State a conclusion that can be drawn from the statements given using the property indicated. LM NO Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate 2

3 Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate 3

4 Over Lesson 2 7 State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate. A. WX > WZ B. XW + WZ = XZ C. XW + XZ = WZ D. WZ XZ = XW Over Lesson 2 7 State a conclusion that can be drawn from the statements given using the property indicated. LM NO A. B. C. D. 4

5 Content Standards G.CO.9 Prove theorems about lines and angles. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 6 Attend to precision. You identified and used special pairs of angles. Write proofs involving supplementary and complementary angles. Write proofs involving congruent and right angles. 5

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7 Use the Angle Addition Postulate CONSTRUCTION Using a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42. What is the measure of the angle the beam makes with the wall? ceiling 1 2 beam wall m 1 + m 2 = 90 m 1 = m 2 = m 2 = m 2 = 48 Angle Addition Postulate Given Substitution Subtraction Substitution Find m 1 if m 2 = 58 and m JKL = 162. A. 32 B. 94 C. 104 D

8 Use Supplement or Complement TIME At 4 o clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands? Understand Make a sketch. 8

9 Use Supplement or Complement TIME At 4 o clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands? Plan Use the Angle Addition Postulate and the definition of angle bisector. Solve Since the angles are congruent by definition, each angle is 60. Answer: Both angles are 60. QUILTING The diagram shows one square for a particular quilt pattern. If m BAC = m DAE = 20, and BAE is a right angle, find m CAD. A. 20 B. 30 C. 40 D. 50 9

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11 Proofs Using Congruent Comp. or Suppl. Theorems Given: Prove: Given: Proofs Using Congruent Comp. or Suppl. Theorems Prove: Proof: Statements Reasons 1. m 3 + m 1 = 180; 1 and 4 form a linear pair and 4 are supplementary and 1 are supplementary Given 2. Linear pairs are supplementary. 3. Definition of supp s 4. s suppl. to same are. 11

12 In the figure, NYR and RYA form a linear pair, AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that NYR and AXY are congruent (Next Slide) Given: NYR and RYA, AXY and AXZ form linear pairs and RYA AXZ Prove: NYR AXY Statements 1. NYR and RYA, AXY and AXZ form linear pairs. 2. NYR and RYA are supplementary. AXY and AXZ are supplementary. 3. RYA AXZ Reasons 1. Given 2.If two s form a linear pair, then they are suppl. s. 3. Given s supp. to the same 4. NYR AXY 4. or to s? are. 12

13 Use Vertical Angles If 1 and 2 are vertical angles and m 1 = d 32 and m 2 = 175 2d, find m 1 and m 2. Justify each step and 2 are vertical s. 1. Given m 1 = m 2 4. m 1= d 32; m 2 = 175 2d 5. d 32 = 175 2d 6. 3d 32 = d = d = m 1= m 2 = m 1= m 2 = 37 Answer: m 1 = 37 and m 2 = Vertical Angles Thm 3. Definition of s 4. Given 5. Substitution 6. Addition Property 7. Addition Property 8. Division Property 9. Substitution 10. Substitution 13

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