Lphillips Geom Ans

10.08.09
A. All poodles are dogs.
1. (if-then) If an animal is a poodle, then it is a dog. True.
2&3. (converse) If an animal is a dog, then it is a poodle. False-Jimbo is a dog, but he's a bulldog.
(inverse) If an animal is not a poodle, then it is not a dog. False-Jimbo, from above, is not a poodle, but he is a dog.
(contrapositive) If an animal is not a dog, then it is not a poodle. True-If it's not even a dog, it can't be a poodle.
B. If 1 angle in a lin pr. is a rt angle, then so is the other.
1. (if-then) If 1 of the angles in a lin. pr. is rt., then the second angle is rt. True
2&3. (converse) If an angle is a rt. angle, then it is in a lin. pr. with another rt. angle. False-The angles don't have to even be adjacent.
(inverse) If an angles is not in a lin. pr. and is rt., then a second angle cannot be rt. False-Again, the angles don't have to even be adjacent.
(contrapositive)If an angle is not right, then it must not be in a linear pair with a right angle. True-If an angles is not 90 degrees, it's partner in the linear pair would have to be the leftover out of 180 degrees.
C. The sum of the measures of the angles in a triangle is 180.
1. (if-then) If angleA, angleB, and angleC are the 3 angles of a triangle, then the sum of their measures must be 180 degrees.
2&3. (converse) If the sum of the measures of 3 angles is 180 degrees, then they must the 3 angles of a triangle. False-The might be adjacent, not in a triangle.
(inverse) If 3 angles are not in a triangle, then they must not have a sum of 180 degrees.
(contrapositive) If 3 angles do not have a sum of 180 degrees, then they cannot be the angles in a triangle. True-Because the angles of a triangle must have a sum of 180.

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