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Properties of Equality and Proving Segment & Angle Relationships

Properties of Equality and Proving Segment & Angle Relationships. Section 2-6, 2-7, 2-8. Remember!. The Distributive Property states that a ( b + c ) = a b + a c. Properties of Equality. Segment Addition Postulate. If B is between A and C, then AB + BC = AC

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Properties of Equality and Proving Segment & Angle Relationships

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  1. Properties of Equality and Proving Segment &Angle Relationships Section 2-6, 2-7, 2-8

  2. Remember! The Distributive Property states that a(b + c) = ab + ac. Properties of Equality

  3. Segment Addition Postulate • If B is between A and C, then AB + BC = AC Converse: If AB + BC = AC, then B is between A and C. A B C

  4. Example: Solving an Equation in Geometry Write a justification for each step.

  5. Example: Solving an Algebraic Equation Write a justification for each step. 3(x - 2) = 42

  6. Statement Reason Example: Proving an Algebraic Conditional StatementWrite a justification for each step.If 3(x - 5/3) = 1, then x=2

  7. Angle Addition Postulate • If R is in the interior of PQS, then mPQR + mRQS = m PQS. • Converse: If mPQR + mRQS = m PQS, then R is in the interior of PQS P R Q S

  8. Segment and Angle Congruence Theorems - Congruence of Segments (or Angles) is Reflexive, Symmetric and Transitive

  9. Example: Identifying Property of Equality and Congruence Identify the property that justifies each statement. A. QRS  QRS B. m1 = m2 so m2 = m1 C. AB  CD and CD  EF, so AB EF. D. 32° = 32° Reflex. Prop. of . Symm. Prop. of = Trans. Prop of  Reflex. Prop. of =

  10. Practice Complete each sentence. 1.If the measures of two angles are ? , then the angles are congruent. 2. If two angles form a ? , then they are supplementary. 3. If two angles are complementary to the same angle, then the two angles are ? . equal linear pair congruent

  11. Additional Angle Theorems that You Should Know • Supplement Theorem – If two angles form a linear pair, then they are supplementary angles. • Complement Theorem – If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

  12. Three More Angle Theorems that You Should Know • Angles supplementary to the same angle, or to congruent angles, are congruent. • Angles complementary to the same angle, or to congruent angles, are congruent. • Vertical Angles Theorem – If two angles are vertical angles, then they are congruent.

  13. Right Angles Theorems that Are Important: • Perpendicular lines intersect to form four right angles. • All right angles are congruent. • Perpendicular lines form congruent adjacent angles. • If two angles are congruent and supplementary, then each is a right angle. • If two congruent angles form a linear pair, then they are right angles.

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