1 / 8

Bell Work

Bell Work. If a line bisects a segment, then the line intersects the segment only at its midpoint. 1. Write the two statements that form each biconditional : A line bisects a segment if and only if the line intersects the segment only at its midpoint.

pahana
Download Presentation

Bell Work

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bell Work If a line bisects a segment, then the line intersects the segment only at its midpoint • 1. Write the two statements that form each biconditional: • A line bisects a segment if and only if the line intersects the segment only at its midpoint. • An integer is divisible by 100 if and only if its last two digits are zero. • 2. Use the law of detachment and law of syllogism to make conclusions. If you cannot make a conclusion, tell why. • If a mountain is the highest in Alaska, then it is the highest in the United States. If an Alaskan mountain is more than 20,300 ft high, then it is the highest in Alaska. Alaska’s Mount McKinley is 20,320 ft high. If a line intersects a segment only at its midpoint, then the line bisects the segment. If an integer is divisible by 100, then its last two digits are zero If an integers last two digits are zero, then it is divisible by 100 Alaska’s Mount McKinley is the highest in the United States.

  2. Review of Deductive Reasoning and Biconditionals September 27, 2011

  3. Biconditionals and Definitions • Is each statement below a good definition? If not, explain. • Two rays intersect if and only if they lie in the same plane. ✔ Yes, because it is is a biconditional statement • A rectangle is a quadrilateral with four congruent angles. ✗ No, because a rectangle is not the only quadrilateral with four congruent angles. • Write each statement as a biconditional. • A square is a rectangle with four congruent sides. A shape is a square if and only if it is a rectangle with 4 congruent sides

  4. Write each statement as a biconditional. • An equilateral triangle is a triangle with three congruent angles A triangle is equilateral if and only if it has three congruent angles • The conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional. • If a number is divisible by 2, then the number is even. Converse: If a number is even, then it is divisible by 2. TRUE Biconditional: A number is divisible by 2 if and only if it is even.

  5. Converse, Inverse, Contrapositive • Write the converse, inverse, and contrapositive of the given conditional statement. Determine the truth value of all three statements. If a statement is false, give a counterexample. • If two angles are supplementary, then their measures sum to 180. Converse: If 2 angles measures sum to 180, then they are suppl. Inverse: If two angles are not suppl., then their measures do not sum to 180. Contrapositive: If 2 angles measures do not sum to 180, then they are not suppl. • If the temperature outside is below freezing, then ice can form on the sidewalks. Converse: If ice can form on the sidewalks, then the temp. outside is below freezing. Inverse: If the temp. outside is not below freezing, then the ice cannot form on the sidewalks. Contrapositive: If ice cannot form on the sidewalks, then the temp. outside is not below freezing

  6. Law of detachment and syllogism • If possible, use the Law of Detachment to make a conclusion. If it is not possible to make a conclusion, tell why. • If a parallelogram has four congruent sides, then the parallelogram is a rhombus. The parallelogram has four congruent sides. CONCLUSION: The parallelogram is a rhombus. • If x > 7, then |x| > 7.x < 7 CONCLUSION: |x| < 7

  7. If possible, use the Law of Syllogism to make a conclusion. If it is not possible to make a conclusion, tell why. • To take Calculus, you must first take Algebra 2. To take Algebra 2, you must first take Algebra 1. CONCLUSION: To take Calculus you must take Alg. 1 • If a tree has ragged bark, then the tree is unhealthy. If a tree has ragged bark, then the tree might be a birch tree. CONCLUSION: Law of Syllogism cannot be used. The same hypothesis is used with different results.

  8. Quiz • Use the law of detachment to make a conclusion. If you cannot tell me why: • 4. If a triangle has two congruent sides, then the triangle is isosceles. In DEF it has 2 congruent sides., • Use the law of syllogism to make a conclusion. If you cannot tell me why: • 5. If a polygon is a square, then it has exactly four congruent angles. If a polygon has exactly four congruent angles, then it is a rectangle. • Is this a good definition? • 6. A hexagon is a polygon with exactly six sides. • Write as a conditional statement. If conditional is true, write converse. If converse is true, write biconditional statement. If converse is false tell me why. • 1. Two complementary angles form a right angle. • 2. If a quadrilateral is a square, then the quadrilateral has four congruent angles. • Write the converse, inverse, and contrapositive of the statement. Tell me whether the statement is true or false for each. • 3. If a triangle is scalene, then the triangle has no congruent sides.

More Related