If two non parallel lines are perpendicular to two other straight lines , each to each . Show that the acute angle between the first pair of lines is equal to the acute angle between the second pair of lines.
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To show that the acute angle between the first pair of lines is equal to the acute angle between the second pair of lines, we can start by drawing a diagram.
First, draw two straight lines (Line A and Line B) that are not parallel, intersecting at point O. Then, draw two other straight lines (Line C and Line D) that are perpendicular to Line A and Line B, respectively. The intersection points between Line A and Line D, as well as Line B and Line C, will be points of interest.
Now, let's consider the acute angles formed. We need to show that the acute angle between Line A and Line D is equal to the acute angle between Line B and Line C.
To do this, we must make use of some geometry properties. Specifically, we will use the fact that when two intersecting lines form adjacent angles (angles that share a common side and a common vertex) that are right angles, those angles are called "vertical angles" and are congruent (equal).
In our diagram:
- Angle AOC and Angle DOB are vertical angles (since they share a common side, Line OD, and a common vertex, point O).
- Angle AOC is the acute angle between Line A and Line D.
- Angle DOB is the acute angle between Line B and Line C.
Because vertical angles are congruent, we can conclude that Angle AOC is congruent to Angle DOB.
Hence, the acute angle between the first pair of lines (Line A and Line D) is equal to the acute angle between the second pair of lines (Line B and Line C).