Which of the following statements is true?Select one of the options below as your answer: A. A 25o angle is congruent to a 25o angle. B. Two intersecting lines form two pairs of congruent angles. C. It is possible for congruent angles to add up to 90o. D. All of the above are true.
Which of the following statements is true?Select one of the options below as your answer:A. A 25o angle is congruent to a 25o angle. B. Two intersecting lines form two pairs of congruent angles. C. It is possible for congruent angles to add up to 90o. D. All of the above are true.
To determine which of the statements is true, let's go through each option:
A. A 25° angle is congruent to a 25° angle.
To check the validity of this statement, we need to understand the concept of congruent angles. Congruent angles have the same measure, meaning they have the same number of degrees. In this case, both angles are 25°, so they have the same measure. Therefore, option A is true.
B. Two intersecting lines form two pairs of congruent angles.
To verify this statement, we can draw two intersecting lines and examine the angles they create at the intersection. When two lines intersect, they form four angles around the point of intersection. These angles are called vertically opposite angles, and they are always congruent, meaning they have the same measure. Hence, option B is true.
C. It is possible for congruent angles to add up to 90°.
To verify this statement, we need to understand the properties of congruent angles. Congruent angles have the same measure, meaning they are equal in degrees. If two congruent angles add up to 90 degrees, each angle must measure 45 degrees. However, congruent angles can only add up to a multiple of their measure. In this case, since the angles measure the same (45 degrees), the sum of two congruent angles is 90 degrees, which is indeed possible. Therefore, option C is true.
D. All of the above are true.
Based on our analysis, we determined that options A, B, and C are all true. Hence, option D, which states that all the statements are true, is the correct answer in this case.