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Understanding Conditional Statements in Geometry

Learn to write inverse, converse, and contrapositive of conditional statements with examples and practice problems in geometry.

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Understanding Conditional Statements in Geometry

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  1. Chapter 2 Test Review

  2. Write the inverse, converse, contrapositive of the conditional statement • IF it is snowing, then the temperature is below 32 °F. Inverse:If it is not snowing, then the temperature is not below 32 °F. Converse:If the temperature is below 32 °F, then it is snowing Contrapositive:If the temperature is not below 32 °F, then it is not snowing

  3. Write the inverse, converse, contrapositive of the conditional statement • IF I ride on the Ferris wheel, then I am not afraid of heights Inverse:If I do not ride on the Ferris wheel, then I am afraid of heights Converse:If I am not afraid of heights, then I ride on the Ferris wheel Contrapositive:If I am afraid of heights, then I do not ride on the Ferris wheel

  4. Write the inverse, converse, contrapositive of the conditional statement • IF two lines are parallel, then the two lines are in the same plane Inverse: If two lines are not parallel, then the two lines are not in the same plane Converse:If the two lines are in the same plane, then two lines are parallel Contrapositive: If the two lines are not in the same plane, then two lines are not parallel

  5. Write the inverse, converse, contrapositive of the conditional statement • IF a point is on segment AB, then it is on ray AB Inverse: If a point is not on segment AB, then it is not on ray AB Converse:If a point is on ray AB, then a point is on segment AB Contrapositive: If it is not on ray AB, then a point is not on segment AB

  6. 1 2 3 Determine whether the biconditional statement is true or false • 1 and 2 are supplementary if and only if they form a linear pair • True • 1 and 2 are congruent if and only if 1  3 • True

  7. Name the property used to make the conclusion. Multiplication Prop of = • x = x • If x = 4 and y = 2x, then y = 8. • IF x = 11, then x – 1 = 10 • If x = y, and y=z then x= z Reflexive prop of = Substitution Prop of = Subtraction Prop of = Transitive Prop of =

  8. GM = GE + EM 28 = 4x + 9 + 3x – 2 28 = 7x + 7 21 = 7x 3 = x AB = CD 5x – 8 = 3x + 20 2x – 8 = 20 2x = 28 x = 14 Solve for the variable using the given information 18. GM = 28 4x + 9 3x - 2 5x - 8 3x + 20

  9. Statements Reasons Write a Two Column Proof Given: AB = BC 1. AB = BC 1. Given 2.AC = AB + BC 2. Segment Add Prop 3.AC = BC + BC 3. Substitution 4.AC = 2BC 4. Substitution 5. Multiplication Prop of =

  10. Statements Reasons Write a Two Column Proof Given: 1 and 3 are a linear pair 2 and 3 are a linear pair Prove: m1 = m2 Without using vertical angle theorem 3 1 2 • 1 and 3 are a linear pair • 2 and 3 are a linear pair 1. Given 2. Linear Pair Psotulate 2. 1 and 3 are supplementary 2 and 3 supplementary 3.1  2 3.  supplements theorem 4.m1 = m2 4. Def  Angles

  11. HW #25Pg 118-120 1-21

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