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Some Proofs That Need Help

  1. Mar 4, 2006 #1
    1. The angles at the base of a triangle are 35° and 65° respectively. If the vertical angle is bisected, calculate the angles that the bisector makes with the base.

    First of all, I don't know what is a veritcal angle but I assumed it was the other angle in the triangle. In that case, it was pretty easy, using Angle Sum Triangle Theory, I got 105 and 75. Can someone confirm?

    2. The point P lies within the angle ABC and is equidistant from AB and BC. Prove that PB bisects the ∠ABC.

    This one I'm struggling with. Especially since the distance PB is equidistant with the two sides is always changing.

    3. State the converse of the following:
    a. If the sum of the angles in a closed figure is 180 degrees, then the figure is a triangle
    b. If the vegetable is green, then it is a lettuce
    c. If a month has 28 days, then it is February
    d. If an animal has four legs and a tail, then it is a cat
    e. If all answers on a test are correct, then no errors have been made

    Straight-forward and I have answers, just would like to verify them.

    4. A fence post 4.5 m high casts a shadow of 2.75 m. At the same time a nearby lamp post cast a shadow 13.75 m in length. Find the height of the lamp post.

    No clue.
  2. jcsd
  3. Mar 4, 2006 #2


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    Question 1 is correctly answered.
    For question 2, do you see why the thing you're asked to prove is true? Draw a diagram, it should be intuitive. Hint: look for two congruent triangles.
    For question 3, you haven't given any answers, so there's nothing for us to verify.
    For question 4, think about similar triangles.
  4. Mar 5, 2006 #3
    I didn't type out answers for 3 because they were long but here's what I got.

    a. If a triangle is a closed figure, then the sum of the angles is 180 degrees.
    b. If a lettuce is a vegetable, then it is green.
    c. If it is February, then the month has 28 days.
    d. If an animal is a cat, then it has four legs and a tail.
    e. If no errors are made on a test, then all answers are correct.

    Also, if both the conditional and converse are true, which I had for a. and e., what are the biconditional statements?
  5. Mar 5, 2006 #4


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    If they were too long for you to type up, why should anyone else type them up? Your answers to a, b, and c are wrong. To see this, look at question a and your answer to it. In particular, look at the antecedents of both statements, and notice how they relate in structure. Do the same for b. (I would say do the same for c, but it's not as obvious what's wrong, although the problem is the same as it is in a and b). Now, do the same thing for d. The relationship between the consequents of question d and your answer to d is a good one, and in a, b, and c, you have that relationship "backwards."

    You're correct that a. and e. are the only ones where the conditional and its converse are true. What do you mean "what are the biconditional statements?" Do you know what a biconditional statement is? It's a "... if and only if ..." statement.
  6. Mar 5, 2006 #5
    You're absolutely right that I shouldn't have expected anyone to do the question for me.

    So, after revising, here are my new statements.

    a. If closed figure is a triangle, then the sum of the angles is 180 degrees.
    b. If a vegetable is a lettuce, then it is green.
    c. If the month is February, then it has 28 days.\

    Here are my biconditional statements for a. and e.:

    a. A closed figure is a triangle if and only if the sum of the angles is 180 degrees.

    e. All answers are correct on a test if and only if no errors have been made.
  7. Mar 6, 2006 #6


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    a, b, and c are correct now, and your biconditionals are correct.
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