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Welcome back…hope you had a wonderful break!

Welcome back…hope you had a wonderful break!. Bellringer …Monday (Everyone: new sheet of GRAPH paper, label with name, date) Graph the line segment & find its length: T (4, -3) H (-5, 2). Properties of Equality. Addition Property: If a=b, then a + c= _____.

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Welcome back…hope you had a wonderful break!

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  1. Welcome back…hope you had a wonderful break! Bellringer…Monday (Everyone: new sheet of GRAPH paper, label with name, date) Graph the line segment & find its length: T (4, -3) H (-5, 2)

  2. Properties of Equality • Addition Property: If a=b, then a + c= _____. • Subtraction Property: If a=b, then a – c= _____. • Multiplication Property: If a = b, then a*c = ____. • Division Property: If If a = b and c ≠ 0, then

  3. Properties of Equality ( ) or Congruence ( ) Reflexive Property of __________: a = a… <A <A Symmetric Property of _________: If a = b, then b = a. If < A < B, then <B <A. Transitive Property of __________: If a = b and b = c, then _______. If < A < B and < B < C, then < A < C.

  4. Definition of congruent angles

  5. Definition of Right Angles:

  6. Prove it! Statements: Reasons: 1. <A is a right angle. 1. 2. <B is a right angle. 2. 3. m<A = 90° 3. 4. 4.Definition of right angle. • 5.Substitution. • <A < B 6. Definition of congruent angles.

  7. If <A and <B are supplementary and < B and < C are congruent. Prove that m<A + m<C=180*. Statements Reasons • <A & <B are supplementary 1. Given • <B & <C are congruent 2. Given • m<A + m<B =180* 3. Def. of supplementary angles • m<B = m<C 4. Def. of congruent angles • m<A + m<C = 180* 5. Substitution

  8. Jumbled Proofs Packet Get them in order: • Write in correct order (same or different page) • Cut & paste in correct order on another page

  9. COW Day….math XL #4 (proofs)

  10. Bellringer…Tuesday COPY the following and DRAW a picture showing the points are collinear: Given: H, I, J, and K are collinear points HJ = IK Prove: HI = JK and that the same segments are congruent.

  11. Conditional Statements • A statement with two parts: hypothesis and conclusion IF… THEN…

  12. If you vote in the election, then ____________________. (let’s just name one option here, not all requirements)

  13. Converse • Switch (transpose) the hypothesis and conclusion.

  14. Inverse • Negate (____________) the hypothesis and conclusion of a conditional statement ***Use the original statement here!***

  15. Contrapositive • Negate both the hypothesis and conclusion of the converse ***Inverse of the converse***

  16. If it is snowing, then it is cold.

  17. Which is true??? Converse: If it is cold, then it is snowing. Inverse: If it is not snowing, then it is not cold. Contrapositive: If it is not cold, then it is not snowing.

  18. Write the three other statements for the statements below. Then tell whether each statement is true (T) or false (F). • If a polygon is a triangle, then the sum of the measures of its interior angles is 180*. • If you drive a car, then you are at least 16 years old. • If two angles are vertical angles, then they are congruent.

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