Converse — Grade 7 Math, what it means and where it is taught
If a2 + b2 = c2, then the triangle must be right-angled.
Taught in Grade 7 Math.
Where it is taught
Practise this idea
4 questions in the course bank use Converse, in How to Write a Proof.
Problem 1
Write the converse of "if it rains, the ground is wet".
Worked answer
if the ground is wet, it rains
Original: if P then Q
Converse: if Q then P
Problem 2
Is the converse of "if two angles are vertical, they are congruent" true? Answer yes or no.
Worked answer
no
Converse: if two angles are congruent, they are vertical.
The base angles of an isosceles triangle are congruent but not vertical.
So the converse is false.
Problem 3
If "if P then Q" is true, which of these is also always true?
- If not Q then not P
- If Q then P
- If not P then not Q
- None of these
Worked answer
If not Q then not P
The contrapositive is always true with the original.
The converse and inverse are not.
Problem 4
The converse of the Pythagorean theorem is true. What does it let you conclude?
Worked answer
the triangle is right-angled
If a2 + b2 = c2 with c longest, then the triangle has a right angle.
It is a genuine theorem, proved separately.