Converse Practice Sheet
Write a converse for the given conditional statement. Then, assuming the original statement is true, decide if the converse must be true or not. If true rewrite using “iff” statement.
1. It two lines intersect, then vertical angles are congruent.
If vertical angles are congruent then two lines intersect. (True)
Vertical angles are congruent iff two lines intersect.
2 .If a polygon is a square, then it is a rectangle.
If a polygon is a rectangle then it is a square. (False)
3. If the shape has three angles, it is a triangle.
If it is a triangle it has three angles. (True)
A shape has three angles iff it is a triangle.
4. If and are vertical angles, then .
If , then and are vertical angles. (False)
5. If n is an odd integer and m is an even integer, then mn is even.
If mn is even then n is an odd integer and m is an even integer (False)
6. If x 3 then x < 4.
If x < 4, then x 3. (False)
7. If a polygon is a rectangle, then it has four 90 angles.
If a polygon has four 900 angles then it is a rectangle. (False - could be six sided with four 900 angles)
8. If it rains, then the ground is wet.
If the ground is wet then it is raining. (False - could be a sprinkler)
9. If two triangles are congruent, then they have the same area.
If two triangles have the same area, then they are congruent (False)
10. If ∆ ABC is an obtuse triangle, then mA + mB + mC = 180.
If mA + mB + mC = 180, then ∆ ABC is an obtuse triangle. (False - could be acute)
11. Things which are equal to equal things are equal to each other.
If things are equal to each other then they are equal to equal things. (True).
Things are equal to equal things iff they are equal to each other.
12. If a man lives in London, he lives in England.
If a man lives in England, then he lives in London. (False)
13. If a triangle is equilateral, it is also isosceles.
If a triangle is isosceles, then it is also equilateral. (False)
14. All straight angles are equal.
All equal angles are straight (False)
15. A right angle is half a straight angle.
If an angle is half a straight angle then it is a right angle (True)
An angle is half a straight iff it is a right angle.
16. Two angles are supplementary, if their sum is 180°.
If the sum of two angles is 180°, then they are supplementary angles. (True)
The sum of two angles is 1800 iff they are supplementary angles.
17. If two triangles are congruent, their corresponding angles are equal.
If two triangles have equal corresponding angles, then they are congruent (False - they are similar)
18. Any point on the perpendicular bisector of AB is equidistant from A and B.
Any point that is equidistant from A and B is on a perpendicular bisector of segment AB. (True)
A point is equidistant from A and B iff it is on a perpendicular bisector of the segment AB.