Question

Which of the following statements is true? A. Congruent angles have the same measure. B. Congruent angles are complementary. C. Congruent angles are supplementary. D. Vertical angles are not congruent.

Answer 1

The statement 'Congruent angles have the same measure' is true. Congruent angles are equal in measure, but this doesn't mean they must be complementary (adding up to 90 degrees) or supplementary (adding up to 180 degrees). Vertical angles are congruent.

Step-by-step explanation:

The statement that is true is A. Congruent angles have the same measure. Congruent angles are angles that are equal in measure. For example, if two angles are both 45 degrees, they are congruent. This does not necessarily mean that congruent angles are complementary or supplementary. Complementary angles are two angles that add up to 90 degrees, while supplementary angles add up to 180 degrees. Vertical angles, which are the angles opposite each other when two lines cross, are always congruent. Therefore, statement D is incorrect as vertical angles are congruent.

Understanding the relationships and distinctions between congruent, complementary, and supplementary angles is important in geometry and helps in solving various problems related to angle measurements. Furthermore, congruent shapes and angles are a foundational concept in geometry that applies to various theorems and principles.

Answer 2

A. Congruent angles have the same measure.

Step-by-step explanation:

In geometry, 2 objects are congruent if they have the same shape. As such, congruent angles are formed from such shapes. Irrespective of the unit of measurement (in degrees or radians), congruent angles are equal.

This is independent of the direction of the angles.

Hence the right option is

A. Congruent angles have the same measure.