Which of the following statements are true?
(1 point)
Responses
If two angles form a linear pair, then the angles are supplementary.
If two angles form a linear pair, then the angles are supplementary.
If two angles are right angles, then the angles are complementary.
If two angles are right angles, then the angles are complementary.
If two angles have the same measure, then the angles are congruent.
If two angles have the same measure, then the angles are congruent.
If two angles are supplementary, then the angles are acute.
None of the statements are true.
1. If two angles form a linear pair, then the angles are supplementary. - True. The definition of a linear pair is that the angles are adjacent and their sum is equal to 180 degrees, which is the definition of supplementary angles.
2. If two angles are right angles, then the angles are complementary. - False. Right angles are always congruent, but complementary angles are two angles that add up to 90 degrees.
3. If two angles have the same measure, then the angles are congruent. - True. Congruent angles have the same measure, so if two angles have the same measure, they are congruent.
4. If two angles are supplementary, then the angles are acute. - False. Supplementary angles are two angles that add up to 180 degrees, but they can be acute, obtuse, or right angles.
The true statements among the given options are:
1) If two angles form a linear pair, then the angles are supplementary.
2) If two angles have the same measure, then the angles are congruent.
The other two statements are not true:
3) If two angles are right angles, then the angles are complementary.
This statement is false because two right angles add up to 180 degrees, making them supplementary, not complementary.
4) If two angles are supplementary, then the angles are acute.
This statement is also false because supplementary angles can have a sum of 180 degrees, but they can be acute, obtuse, or right angles.