rewrite this essay

Question

Statement Reason
Given:
𝑎
∥
𝑏
a∥b and
𝑒
∥
𝑓
e∥f Given
∠a = ∠b Corresponding angles of parallel lines
∠e = ∠f Corresponding angles of parallel lines
∠a + ∠e = 180° Opposite angles of a parallelogram
∠b + ∠f = 180° Opposite angles of a parallelogram
∠a + ∠e = ∠b + ∠f Substitution
𝑎
𝑏
‾
ab
≅
𝑒
𝑓
‾
ef
​
Vertical angles are congruent
This proof demonstrates that opposite sides of the parallelogram are congruent because they share the same measure due to corresponding angles formed by parallel lines.

Answer 1

This proof shows that when a pair of parallel lines intersect a transversal, the corresponding angles formed are congruent. This is because when two lines are parallel, the corresponding angles are equal. In a parallelogram, opposite angles are supplementary, meaning they add up to 180 degrees. By substitution, we can see that the sum of the angles on one side is equal to the sum of the angles on the other side. Therefore, the opposite sides of the parallelogram are congruent because they share the same measure due to corresponding angles formed by parallel lines. This also applies to vertical angles, which are congruent in this case.