Since line EF is parallel to line GH, angle 1 = angle 2.
Since line FG is parallet to line HE, angle 3 = angle 4.
Give reasons to support your answers.
To support the given statements, we need to understand two important angle relationships: alternate interior angles and corresponding angles.
1. Angle 1 and Angle 2:
Explanation: When two parallel lines are intersected by a transversal (a line that crosses two other lines), the resulting angles formed on opposite sides of the transversal are known as alternate interior angles.
Reasoning: By the given information, line EF is parallel to line GH. When these two lines are intersected by the transversal line GH, Angle 1 and Angle 2 are formed on opposite sides of the transversal. Since alternate interior angles are congruent for parallel lines, Angle 1 must be equal to Angle 2.
2. Angle 3 and Angle 4:
Explanation: Similarly, when two parallel lines are intersected by a transversal, the resulting angles formed at corresponding positions (i.e., in the same relative positions) are known as corresponding angles.
Reasoning: According to the given information, line FG is parallel to line HE. When these two lines are intersected by the transversal line GH, Angle 3 and Angle 4 are formed in corresponding positions on opposite sides of the transversal. Corresponding angles are also congruent for parallel lines, so Angle 3 must be equal to Angle 4.
In summary, the reason why Angle 1 equals Angle 2 is due to the concepts of alternate interior angles with parallel lines. The reason why Angle 3 equals Angle 4 is based on the concept of corresponding angles with parallel lines.