prove that two lines in a plan which ar perpandicular to the same given line the plan ar parallel to each other

Answer

To prove that two lines in a plane which are perpendicular to the same given line are parallel to each other, we can follow these steps:

### Step 1: Identify the Lines
Let’s denote the given line as line L. We have two lines, line M and line N, which are both perpendicular to line L.

### Step 2: Draw the Lines
Draw line L horizontally. Then, draw line M such that it forms a 90-degree angle with line L. Next, draw line N also such that it forms a 90-degree angle with line L.

### Step 3: Measure the Angles
Since both lines M and N are perpendicular to line L, we know that:
- The angle between line L and line M (let's call this angle 1) is 90 degrees.
- The angle between line L and line N (let's call this angle 2) is also 90 degrees.

### Step 4: Compare the Angles
Now, we can compare angle 1 and angle 2:
- Measure of angle 1 = 90 degrees
- Measure of angle 2 = 90 degrees

### Step 5: Establish Corresponding Angles
Since angle 1 and angle 2 are both equal to 90 degrees, we can say:
- Angle 1 = Angle 2

### Step 6: Apply the Corresponding Angles Postulate
According to the Corresponding Angles Postulate, if two lines are cut by a transversal (in this case, line L), and the corresponding angles are equal, then the two lines (M and N) are parallel.

### Conclusion
Since angle 1 = angle 2, we conclude that line M is parallel to line N.

### Final Statement
Thus, we have proved that two lines in a plane which are perpendicular to the same given line are parallel to each other.

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