2. ∠4 ≅ ∠1
8a. Choose the correct reason:
a. Linear Pair Postulate
b. Angle Addition Postulate
c. Vertical Angle Postulate
d. Congruent Angle Postulate
Answer: d. Congruent Angle Postulate
Question can't be answered because of missing data.
e.g. are there some kind of parallel lines ?
where are ∠4 and ∠1 ?
The correct reason to justify that ∠4 ≅ ∠1 is the Vertical Angle Postulate, which states that vertical angles are congruent.
To determine the correct reason for the given statement, we need to understand the definitions and postulates related to angles.
1. Linear Pair Postulate: Two angles that form a linear pair are supplementary, meaning their measures add up to 180 degrees. In a linear pair, the angles are adjacent (share a common side) and their non-common sides form a straight line.
2. Angle Addition Postulate: This postulate states that if there is a point P inside an angle, then the measure of the larger angle is equal to the sum of the measures of the two smaller adjacent angles that form it.
3. Vertical Angle Postulate: Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They are congruent, meaning their measures are equal.
Given that ∠4 ≅ ∠1, we are comparing two specific angles.
To determine the correct reason, let's analyze the options:
a. Linear Pair Postulate: This postulate deals with angles that form a straight line. However, there is no information given about the angles forming a straight line or being supplementary. Therefore, this reason is not applicable.
b. Angle Addition Postulate: This postulate deals with the sum of angles if there is a point inside an angle. However, there is no mention of a point inside the angle or any reference to adding angles. So, this reason is also not applicable.
c. Vertical Angle Postulate: This postulate states that when two lines intersect, the angles formed are congruent (or equal). This seems to be the most relevant postulate in this context since we are comparing the angles ∠4 and ∠1. Therefore, the correct reason for the given statement is the Vertical Angle Postulate (c).
In conclusion, the correct reason for the statement ∠4 ≅ ∠1 is the Vertical Angle Postulate.