# Geometry

posted by .

1. Explain whether the following statement is a valid definition: “A 150° angle is an obtuse angle.” Use the converse, biconditional, and at least one Euler diagram to support your answer.

2. Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deductive reasoning and describe how each can help you develop and prove theorems.

• Geometry -

“A 150° angle is an obtuse angle.”

We will represent the proposition as follows:
p=the angle is 150°
q=it is an obtuse angle

The above proposition (may or may not be true) is equivalent to:
p->q (If the angle is 150°, it is an obtuse angle).

The converse is
q->p (If an angle is obtuse, it is 150°)

The biconditional is:
p<->q (If the angle is 150°, it is an obtuse angle, and if an angle is obtuse, it is 150°)

We can see that p->q is true, but q->p is not. Consequently p<->q is not true, because
p<->q ≡ p->q ∧ q->p,
so if q->p is false, p<->q is also false.

The Euler diagram for p->q is a small circle P completely inside a bigger circle Q, so that whenever p is true, q has to be true.

Try to draw the Euler diagram for the other two cases.

## Similar Questions

1. ### geometry

Rewrite the biconditional as a conditional statement and its converse and then determine if the biconditional is an accurate definition: Two angles are supplementary if and only if they form a linear pair conditional:_____________________________ …
2. ### geometry

Refer to the following statement: Two lines are perpendicular if and only if they intersect to form a right angle. A. Is this a biconditional statement?
3. ### Help with deductive reasoning

Determine whether you can use the Law of Syllogism to reach a valid conclusion from each set of statements. 1. If a dog eats Superdog Dog Food, he will be happy. Rover is happy. 2. If an angle is supplementary to an obtuse angle, then …
4. ### geometry

Write the converse of this statement. If two angles are both obtuse, the two angles are equal. Converse: i don't get this please explain
5. ### geometry

If an angle measures more than 90°, then it is an obtuse angle. What is the converse of this statement?
6. ### geometry

If an angle measures more than 90°, then it is an obtuse angle. What is the converse of this statement?
7. ### geometry

obtuse triangle ABC with obtuse angle B. Point D on side AC such that angle BDC is also obtuse. Angle DAB is 2/3 of angle ABD. Angle BCD is 1/5 of angle CBD is 4 more than angle BAD. Find the measure of angle ABC.
8. ### Geometry

Given: obtuse triangle ABC with obtuse angle B. Point D on side AC such that angle BDC is also obtuse. Angle DAB is 2/3 of angle ABD. Angle BCD is 1/5 angle BDC and angle CBD is 4 more than angle BAD. What is the measure of angle ABC?
9. ### Geometry

Explain whether the following statement is a valid definition: “A 30° angle is an acute angle.” Use the converse, biconditional, and at least one Euler diagram to support your answer.
10. ### Geometry

If a conditional and its converse are always true, then the statement is a a. converse. b. conditional. c. biconditional. d. counterexample. I am trying to do some geometry and haven't taken it in a while so can someone please help?

More Similar Questions