Question 21
Start with the theorem “If two angles of a triangle are equal, the triangle is isosceles,” and the following four statements:
$1.$ If two angles of a triangle are not equal, the triangle is not isosceles.
$2.$ The base angles of an isosceles triangle are equal.
$3.$ If a triangle is not isosceles, then two of its angles are not equal.
$4.$ A necessary condition that two angles of a triangle be equal is that the triangle be isosceles.
Which combination of statements contains only those which are logically equivalent to the given theorem?
$1.$ If two angles of a triangle are not equal, the triangle is not isosceles.
$2.$ The base angles of an isosceles triangle are equal.
$3.$ If a triangle is not isosceles, then two of its angles are not equal.
$4.$ A necessary condition that two angles of a triangle be equal is that the triangle be isosceles.
Which combination of statements contains only those which are logically equivalent to the given theorem?