Logic
Postulates
Parallel Lines and Angles
Chapter 1
100
1.Analyze the following statement and determine whether the conjecture is true or false. Explain your reasoning and provide a counterexample for any false conjecture. If <1 and <2 are adjacent angles, then <1 and <2 are complementary.
False, could be supplementary.
100
Directions: Use postulates to determine whether each statement is always, sometimes, or never true. Include a statement or drawing to support answer. Through any two points, there is exactly one line.
Always
100
Identify the relationship between the two indicated angles.
Alternate Exterior
100
If ray KN bisects
y= 27
200
2.Analyze the following statement and determine whether the conjecture is true or false. Explain your reasoning and provide a counterexample for any false conjecture. If line AB and line CD are coplanar, then they intersect.
False, they could be parallel lines in the same plane.
200
Directions: Use postulates to determine whether each statement is always, sometimes, or never true. Include a statement or drawing to support answer. There are exactly three collinear points contained on a plane.
Sometimes
200
If <3 = 67*, what is the m<5?
113
200
The supplement of an angle is six less than twice the measure of the angle. What is the measure of each angle?
62 and 118
300
4.Given statements p and q, state the conditional and converse. Determine the truth values of all 4 statements. For any false statements, provide a counterexample. p: The dog is a lab. q: He is brown.
Conditional: If the dog is a lab, then he is brown. False: black Converse: If he is brown; then he is a lab. False: Boxer
300
Directions: Use postulates to determine whether each statement is always, sometimes, or never true. Include a statement or drawing to support answer. If two planes intersect, they intersect at a point.
Never
300
Determine the value of x in the picture
17
300
The complement of an angle is 8 more than three times the measure of an angle. What are the measures of each angle?
20.5 and 69.5
400
4.Given statements p and q, state the inverse and contrapositive. Determine the truth values of all 4 statements. For any false statements, provide a counterexample. p: The dog is a lab. q: He is brown.
Inverse: If the dog is not a lab, then he is not brown. False: Could still be brown. Contrapositive: If he is not brown, then he is not a lab. False: Could still be a lab.
400
State the postulate that can be used to show that the statement is true. D, W, and E are coplanar.
Any three points form a plane.
400
Determine the value of x and y in the picture.
x=75, y=110
400
Find the distance between T(-5, 8) and R(2, 9).
sqrt 73
500
Find the folowing given that the conditional is If an angle is 30, then it is acute. Contrapositive: Inverse : Converse:
Contrapositive: If an angle is not acute, then it is not 30. Inverse :If an angle is not 30, then it is not acute. Converse: If an angle is acute, then it is 30.
500
State the postulate that can be used to show that the statement is true. E and W are collinear
Through any two points there is a line.
500
Find the measure of <1 and <2. m<1 = 7x + 14, m<2 = 2x + 4
x=18, <1=140, <2=40
500
Determine the coordinates of F if E(-3, 8) is the midpoint of DF where D is located at (4, 6).
(-10, 10)
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