Mathematics

Grade9

Easy

Question

# Which law of deductive reasoning is being used, if any?

If a triangle is equilateral, then all three sides are congruent.

If all the sides of a triangle are congruent, then the angles opposite them are congruent.

Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

- Law of Detachment
- Law of Syllogism
- Law of the Contrapositive
- Not valid

Hint:

### In deductive reasoning we use facts, definitions and postulates to draw a conclusion. There are two laws under deductive reasoning they are Law of Detachment and Law of Syllogism. Here, we have to determine which of these laws in applied here to draw the conclusion.

## The correct answer is: Law of Syllogism

### In the question it is given that,

1) If a triangle is equilateral, then all three sides are congruent.

2) If all the sides of a triangle are congruent, then the angles opposite them are congruent.

3) Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

Here, we have to determine the law which the above statements obey.

Let statement (1) be p, statement (2) be q and statement (3) be r.

From the given statement we can say that p equals to q and r the conclusion drawn from p and q.

So, the statement (3) is true for statement (1) and (2).

Thus, the above statements obey the Law of Detachment.

Therefore, the correct option is Law of Detachment.

In Law of Syllogism if a statement p equals q and if q equals r, then p equals r whereas in Law of Detachment if a statement p equals q where p is true then q is also true.