<3 ≅ <8
A Alternate Interior Angles Converse
B Same side interior angles
C Transitive Property
D Given
E Vertical angles are congruent
F Symmetric Property
E Vertical angles are congruent
The correct answer for the statement "<3 ≅ <8" is D - Given.
The symbol "≅" represents congruence, which means that the angles <3 and <8 are congruent. In this case, the fact that the angles are congruent is given or stated in the problem. Therefore, the answer is D - Given.
To determine which statement is true in this case, we need to compare the given symbol ≅, which represents congruence, with the relationship between the angles described by the options A-F.
The symbol ≅ is used to indicate that two objects or shapes are congruent, meaning they are exactly the same in shape and size. In this case, we are comparing two angles represented by <3 and <8.
Let's go through each option and see which one matches the given statement:
A) Alternate Interior Angles Converse: This states that if two lines are intersected by a transversal, and the alternate interior angles are congruent, then the lines are parallel. However, this statement does not directly relate to the given information about <3 and <8, so A is not the correct answer.
B) Same Side Interior Angles: This states that if two lines are intersected by a transversal, and the same-side interior angles are supplementary, then the lines are parallel. Again, this statement does not directly relate to the given information about <3 and <8, so B is not the correct answer.
C) Transitive Property: This property states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C. Since we only have one statement about the angles (<3 ≅ <8), the Transitive Property is not applicable here, so C is not the correct answer.
D) Given: This option indicates that the relationship between <3 and <8 is given. Since the statement <3 ≅ <8 is given, this option fits the given information, so D might be the correct answer.
E) Vertical Angles are Congruent: This statement states that when two lines intersect, the pairs of vertical angles formed are congruent. However, we don't have information about vertical angles in the given statement, so E is not the correct answer.
F) Symmetric Property: This property states that if angle A is congruent to angle B, then angle B is congruent to angle A. Again, since we only have one statement about the angles (<3 ≅ <8), the Symmetric Property is not applicable here, so F is not the correct answer.
Based on the analysis above, the correct answer is option D) Given, because it aligns with the given statement that <3 and <8 are congruent.