An if-then statement has a hypothesis (after "if") and a conclusion (after "then"). Swap them for the converse. Negate both for the inverse. Swap and negate for the contrapositive, which always has the same truth value as the original; the other two need not.
Write the converse of: If two angles are vertical, then they are congruent.If they are congruent, then two angles are vertical.
Identify the hypothesis and conclusion: If a number is divisible by 6, then it is divisible by 3.H: a number is divisible by 6; C: it is divisible by 3
Write the converse of: If you live in Texas, then you live in the United States.If you live in the United States, then you live in Texas.
Identify the hypothesis and conclusion: If two angles are vertical, then they are congruent.H: two angles are vertical; C: they are congruent
Write the contrapositive of: If a shape is a square, then it has four equal sides.If it does not have four equal sides, then a shape is not a square.
Identify the hypothesis and conclusion: If an animal is a dog, then it is a mammal.H: an animal is a dog; C: it is a mammal
Write the inverse of: If a triangle is equilateral, then all three angles measure 60°.If a triangle is not equilateral, then the three angles do not all measure 60°.
Identify the hypothesis and conclusion: They are supplementary if two angles form a linear pair.H: two angles form a linear pair; C: they are supplementary
Write the converse of: If an animal is a dog, then it is a mammal.If it is a mammal, then an animal is a dog.
Identify the hypothesis and conclusion: If a figure is a circle, then every point on it is the same distance from the centre.H: a figure is a circle; C: every point on it is the same distance from the centre
Write the converse of: If a point is the midpoint of a segment, then it splits the segment into two congruent parts.If it splits the segment into two congruent parts, then a point is the midpoint of a segment.
Identify the hypothesis and conclusion: If a quadrilateral is a rhombus, then its four sides are congruent.H: a quadrilateral is a rhombus; C: its four sides are congruent
Write the contrapositive of: If it is raining, then the ground is wet.If the ground is not wet, then it is not raining.
Identify the hypothesis and conclusion: It splits the segment into two congruent parts if a point is the midpoint of a segment.H: a point is the midpoint of a segment; C: it splits the segment into two congruent parts
Write the inverse of: If a polygon is a triangle, then its angles add to 180°.If a polygon is not a triangle, then its angles do not add to 180°.
Identify the hypothesis and conclusion: They never meet if two lines are parallel.H: two lines are parallel; C: they never meet
Write the inverse of: If a figure is a rectangle, then its diagonals are congruent.If a figure is not a rectangle, then its diagonals are not congruent.
Identify the hypothesis and conclusion: If two lines are parallel, then they never meet.H: two lines are parallel; C: they never meet
Write the contrapositive of: If two angles form a linear pair, then they are supplementary.If they are not supplementary, then two angles do not form a linear pair.
Identify the hypothesis and conclusion: It ends in 0 if a number is a multiple of 10.H: a number is a multiple of 10; C: it ends in 0
Write the contrapositive of: If a shape is a square, then it has four equal sides.
Swap the two parts, and negate each.
Not four equal sides, so not a square.
The answer is If a shape does not have four equal sides, then it is not a square..
Where students go wrong
Mixing up converse and inverse. Converse swaps, inverse negates; the contrapositive does both.
Also called converse inverse contrapositive, if-then statements, hypothesis and conclusion or logic in geometry.
What you can put on this worksheet
Converse, inverse, contrapositive
Write the converse of: If a number is divisible by 6, then it is divisible by 3.→ If it is divisible by 3, then a number is divisible by 6.
Hypothesis and conclusion
Identify the hypothesis and conclusion: If a number is divisible by 6, then it is divisible by 3.→ H: a number is divisible by 6; C: it is divisible by 3
Questions about these worksheets
Yes. Every conditional statements sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the conditional statements questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: converse, inverse, contrapositive and hypothesis and conclusion. Tick as many as you want and set how many of each, or let it spread them evenly.
Mixing up converse and inverse. Converse swaps, inverse negates; the contrapositive does both.