The statement "The acute interior angles of a right triangle are complementary" is always true.
Reasoning: In a right triangle, one of the interior angles is exactly 90 degrees (the right angle). A triangle, by definition, has a total of 180 degrees in its interior angles. Therefore, if one angle is 90 degrees, the sum of the other two interior angles must be:
\[ 180^\circ - 90^\circ = 90^\circ \]
The two remaining angles in a right triangle are the acute angles. Because their sum is 90 degrees, these two angles are complementary.
In summary, because the sum of the acute angles always equals 90 degrees, the statement is always true.
1 answer