<1 ≅ <8
A Alternate Interior Angles Converse
B Same side interior angles
C Transitive Property
D Given
E Vertical angles are congruent
F Symmetric Property
A Alternate Interior Angles Converse
The statement <1 ≅ <8 is referring to two angles, angle 1 and angle 8. In order to determine the relationship between these angles, we can consider the given options.
Given:
The option "D Given" suggests that the relationship between angle 1 and angle 8 is stated or provided in the question or problem itself. If this is the case, you need to refer to the context or information provided to determine the relationship.
Symmetric Property:
The option "F Symmetric Property" states that if angle 1 is congruent to angle 8, then angle 8 is also congruent to angle 1. However, in the given statement <1 ≅ <8, we don't have any information about the congruence of angle 8 to angle 1. Therefore, we cannot conclude that the relationship between angle 1 and angle 8 is due to the symmetric property.
Alternate Interior Angles Converse:
The option "A Alternate Interior Angles Converse" states that if two lines are cut by a transversal and the alternate interior angles formed are congruent, then the lines are parallel. However, we don't have any information about the lines in the given statement. Therefore, we cannot conclude that the relationship between angle 1 and angle 8 is due to the alternate interior angles converse.
Same Side Interior Angles:
The option "B Same side interior angles" states that if two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel. However, we don't have any information about the supplementary nature of the angles in the given statement. Therefore, we cannot conclude that the relationship between angle 1 and angle 8 is due to the same side interior angles.
Transitive Property:
The option "C Transitive Property" states that if angle 1 is congruent to angle 2, and angle 2 is congruent to angle 3, then angle 1 is congruent to angle 3. In the given statement, we only have information about the congruence between angle 1 and angle 8. Therefore, we cannot conclude that the relationship between angle 1 and angle 8 is due to the transitive property.
Vertical Angles are Congruent:
The option "E Vertical angles are congruent" states that vertical angles formed by intersecting lines are congruent. However, since we don't have any information about intersecting lines in the given statement, we cannot conclude that the relationship between angle 1 and angle 8 is due to the congruence of vertical angles.
Based on the given options and the given statement, none of the indicated properties or relationships can be used to determine the relationship between angle 1 and angle 8.
To determine which statement justifies the congruence of angles <1 and <8, we need to examine the given information.
The symbol "≅" denotes congruence, which means that the two angles are equal in measure.
Option A: Alternate Interior Angles Converse states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. However, this doesn't provide direct justification for the congruence of <1 and <8.
Option B: Same side interior angles refer to angles that are on the same side of the transversal, but not directly opposite to each other. This property doesn't apply here because <1 and <8 are not same side interior angles.
Option C: The Transitive Property of equality states that if a = b and b = c, then a = c. This property is not applicable since we don't have any previous congruent angles that lead to <1 ≅ <8.
Option D: The "Given" statement alone doesn't explain the congruence of <1 and <8. It simply indicates that this information has been provided.
Option E: Vertical angles are congruent property states that when two lines intersect, the vertical angles formed are congruent. However, there is no information given to directly connect <1 and <8 as vertical angles.
Option F: The Symmetric Property of equality states that if a = b, then b = a. This property applies to our scenario since it involves the congruence of angles. Therefore, since the angles in question are given as <1 ≅ <8, we can conclude that <8 ≅ <1 using the symmetric property.
Therefore, the answer is F: Symmetric Property.