Determine whether each conjecture is true or false.Give a counter example for any false conjecture.
Given:Angle 1 and angle 2 are not complementary.angle 2 and angle 3 are complementary.
Conjecture:angle1=angle3
I need help on this..please
write the converse,inverse,and contrapositive of the statement.determine if its true or false,if its false write counterexample.
"If 2 angles are adjacent,then the angles have common vertex.
mudosa
To determine whether the conjecture is true or false, we need a counterexample for a false conjecture:
If angle 1 and angle 2 are not complementary, it means that the sum of their measures is not equal to 90 degrees.
If angle 2 and angle 3 are complementary, it means that the sum of their measures is equal to 90 degrees.
Now, let's assume that angle 1 is 60 degrees and angle 2 is 40 degrees. Since 60 degrees + 40 degrees = 100 degrees, angle 1 and angle 2 are not complementary.
Let's also assume that angle 2 is 50 degrees and angle 3 is 40 degrees. Since 50 degrees + 40 degrees = 90 degrees, angle 2 and angle 3 are complementary.
Therefore, the conjecture that angle 1 is equal to angle 3 is false because there is a counterexample where angle 1 is 60 degrees and angle 3 is 40 degrees.
To determine the truth or falsehood of the conjecture, we need to analyze the given information and look for a counterexample if applicable.
The given information states that angle 1 and angle 2 are not complementary, and angle 2 and angle 3 are complementary.
A counterexample can help us prove the conjecture false. Let's assume angle 1 is 60 degrees, angle 2 is 80 degrees, and angle 3 is 100 degrees. In this scenario, angle 1 and angle 2 are not complementary because their sum is 140 degrees, which is not 90 degrees. Angle 2 and angle 3, on the other hand, are complementary since their sum is indeed 180 degrees. However, looking at the values, angle 1 (60 degrees) is not equal to angle 3 (100 degrees).
Therefore, the conjecture that angle 1 is equal to angle 3 is false, and a counterexample has been provided to support this conclusion.