Question

! Geometry !

Read the following statements.

1. PQR is acute.
2. PQR is isosceles.
3. PQR is right.

Which two statements contradict each other?


2 and 3


None of the statements contradict each other.


1 and 2


1 and 3

Answer 1

1 and 3 contradict each other

An isosceles triangle has 3 acute angles.

**ignore my comments I’m literally contradicting myself

Answer 2

1 and 3 are contradictory

Explanation:

A triangle is acute if all angles are less than 90

A triangle is isosceles if any two angles are congruent.

A triangle is right if one of the angle is 90.

Hence we see that a triangle is acute has all angles less than 90.

So it cannot be simultaneously right triangle.

Thus we find that 1 and 3 are contradictory.

1 and 2 are not contradictory as two acute triangles can be equal and also third is acute.

2 and 3 are not contradictory since when a right triangle has other two angles as 45, 45 then it is isosceles as well as right.

Answer is 1 and 3 are contradictory.