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Geometric Properties

The man who has no imagination has no wings Muhamma d Ali. Geometric Properties. Take a worksheet Finish the Pictures. Postulate 2.10 (Protractor Postulate)

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Geometric Properties

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  1. The man who has no imagination has no wings Muhammad Ali Geometric Properties Take a worksheet Finish the Pictures • Postulate 2.10 (Protractor Postulate) • Given AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of AB, such that the measure of the angle formed is r. • Postulate 2.11 (Angle Addition Postulate) • If R is the interior of PQS, then mPQR + mRQS = mPQS • If PQS, then mPQR + mRQS = mPQS then R is in the interior of PQS B r A P R Q S

  2. Chapter 2.8 Proving Angle Relationships Objective: Continue developing skills writing proofs by proving angle relationships

  3. Angle Theorems • 2.3 Supplement Theorem • If two angles form a linear pair then they are supplementary • 2.4 Complement Theorem • If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary 1 2 m1 + m2 = 180 1 m1 + m2 = 90 2

  4. 2.5 Congruence of Angles • Reflexive Property • m1  m1 • Symmetric Property • m1  m2, then m2  m1 • Transitive Property • m1  m2 and m2  m3, • then m1  m3

  5. Congruent Angle Theorems • 2.9 Perpendicular lines intersect to form four right angles • 2.10 All Right angles are congruent • 2.11 Perpendicular lines form congruent adjacent angles • 2.12. If two angles are congruent and supplementary, then each angle is a right angle • 2.13 if two congruent angles form a linear pair then they are right angles.

  6. Theorems • 2.6 Angles supplementary to the same angle or to congruent angles are congruent. • ’s suppl. to same  or   are  • If m1 + m 2 = 180 and m2 + m 3 = 180, • then m1 =m 3 • 2.7 Angles complementary to the same angle or to congruent angles are congruent. • ’s compl. to same  or   are  • If m1 + m 2 = 90 and m2 + m 3 = 90, • then m1 =m 3

  7. Prove Theorem 2.7 Complementary Angles 1 Statements Reasons Given Definition of Complementary Angles Substitution Reflective Property Subtraction Definition of congruent Angles 1 & 3 are complementary 2 & 3 are complementary m1 + m3 = 90 m2 + m3 = 90 m1 + m3 = m2 + m3 m3= m3 m1 = m2 1  3 Prove the following: Given: 1 & 3 are complementary and 2 & 3 are complementary Prove: 1  3 2 3

  8. Find the Value of the Angle • If 1 and 2 are vertical angles and m1= x and m2= 228 – 3x, find m1 and m 2. 1  2 m1 = m2 x = 228 – 3x +3x +3x 4x = 228 x = 57 m1= 57 m2= 57 1 2

  9. Find the Value of the Angle • If 1 and 2 are vertical angles and m1= d-32 and m2=175 – 2d, find m1 and m 2. 1  2 m1 = m2 d - 32 = 175 – 2d +2d + 32 +32 +2d 3d = 207 d = 69 m1= 69-32 = 37 m2= 37 1 2

  10. Practice Assignment • Page 154 8-30 Every 4th

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