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Geometry 2.1 and 2.2 Conditional and Biconditional Statements
Date ______________
Rewrite each of the following statements in the if-then form. Underline the hypothesis
and circle the conclusion in each statement.
1. All dogs are mammals.
2. All vertical angles are congruent.
3. Two lines intersect in a point.
Write the converse of each of the following statements. Determine if the converse is true
or false. If false, provide a counterexample.
4. If two angles are vertical angles, then they are congruent.
5. If x 2  36 , then x = 6 or x = -6.
6. If two angles form a linear pair, then they are supplementary.
7. If an angle measures 175, then it is an obtuse angle.
Draw a sketch to illustrate each of the following postulates.
1. Through any two points there exists exactly one line.
2. A line contains at least two points.
3. If two lines intersect, then their intersection is exactly one point.
4. Through any three non-collinear points there exists exactly one plane.
5. A plane contains at least three non-collinear points.
6. If two points lie in a plane, then the line containing them lies
in the plane.
7. If two planes intersect, then their intersection is a line.
Rewrite each of the following statements as a bi-conditional statement.
1. Perpendicular lines intersect to form a right angle.
2. Complementary angles have a sum of 90.
3. Three collinear points lie on the same line.
Rewrite each bi-conditional statement as its conditional statement and its converse.
4. Point Y lies between points X and Z if and only if XY + YZ = XZ.
Conditional:
Converse:
5. Two angles are congruent if and only if they have the same measure.
Conditional:
Converse:
6. The car will run if and only if there is gas in the tank.
Conditional:
Converse:
A bi-conditional statement is a true bi-conditional if it’s conditional statement and its
converse are both true. Which of the above bi-conditionals are true bi-conditionals?
Write the converse of each true statement. If the converse is also true, combine the
statements to write a true bi-conditional statement.
7. If you are 15 years old, then you are a teenager.
Converse:
Bi-conditional:
8. If two angles are supplementary, then the sum of their measures is 180.
Converse:
Bi-conditional:
9. If two angles form a linear pair, then they are adjacent.
Converse:
Bi-conditional: