Geometry - Conditional Statements/Proof

posted by .

Rewire each statement as two if-then statements that are converses of each other.

18. Two angles are supplementary if and only if the sum of their measures is 180.

20. (x-4)(x+6) = 0 if and only if x = 4 or x = -6

22. Theorem 2-5 may also be worded in this way: "If alternate interior angles formed by two lines and a transversal are congruent, then the lines are parallel." Write the converse of this statement. Is the converse true?

Tell whether you think each statement is true or false.
If false, draw a diagram that shows a counterexample.
If true, draw a diagram. List, in terms of he dram, what is given and what is to be proved. Do not write a proof.

24. If a triangle has two congruent sides, then the angles opposite those sides are congruent.

26. Two triangles have equal perimeters only if they have congruent sides.

28. If both pairs of opposite sides of a quadrilateral are paralell, then each side is congruent ot the side opposite it.

30. The diagonals of an equilateral quadrilateral are congruent.

In the conditional statement "if p, then q," p is said to be a sufficient condition for q to occur. Similarly, q is said to be a necessary condition for p. In Exercises 32-37 tell whether the first statement is necessary for the second statement, sufficient for it, or both necessary and sufficient for it.

Eg. First Statement and Second Statement

32. x > 4 and x is positive

34. Line l and m do not intersect.

36. A polygon is equilateral.

----------------------------------------------------

38. a) Given: Line AB ll Line DC; Line AD ll Line BC
b) Tell what is given and what is to be proved in the converse of part (a). Then write a proof of the converse.
c) Combine what you have proved in parts (a) and (b) into an if-and-only-if statement.

  • Geometry - Conditional Statements/Proof -

    We do not do a student's assignments.
    How about letting us know what answers you got, and I am sure somebody will tell you how you did.

    I will do one of them for you.

    Two angles are supplementary if and only if the sum of their measures is 180.
    1. Two angles are supplementary if the sum of their measures is 180.
    2. The sum of their measures is 180 if two angles are supplementary.

  • Geometry - Conditional Statements/Proof -

    false

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics (geometry bit)

    h t t p : / / i m g 4 3 . i m a g e s h a c k . u s / i m g 4 3 / 4 7 4 1 / 9 4 7 4 7 1 1 6 . j p g ok the two read angles are equal to each other because they are complementary if i remeber correctly the only thing we can conclude …
  2. Geometry

    Use the Law of Detachment to write a valid conclusion for the given information. 1.If two angles are supplementary, then their measures have a sum of 180. 2.Angle X and Angle Y are supplementary. Would the conclusion be this?
  3. Math

    Find the measures of two supplementary angles if the difference of their measures is 56 degrees I know supplementary angles are the sum of the measure if two angles is 180 degrees but then what is the question asking?
  4. Math

    Part 1: Write two conditional statements for which the converse is true. 1. Statement: 2. Converse: 3. Statement: 4. Converse: Part 2: Write two conditional statements for which the converse is false. 5. Statement: 6. Converse: 7. …
  5. Geometry

    write two conditional statements that make up the following biconditional statement: "Two lines are perpendicular if and only if their intersection creates 4 right angles."
  6. Geometry

    Two angles are supplementary if the sum of their measures is 180∘. If the measure of one angle is 16x degrees, represent the measure of its supplement as an expression of x.
  7. Geometry Check please

    Is the following definition of complementary angles reversible?
  8. Geometry

    Why do complementary and supplementary angles not have to be adjacent?
  9. Math

    So my teacher marked this 0/6 but only told me to correct 2 things. Can some one check over this?
  10. Geometry

    Is the following definiiton of supplementary reversible?

More Similar Questions