Draw a straight line segment of length 5 cm and name  MN .

Construct an angle of 60° at M such that MN is an arm 

Construct the perpendicular at point N

Mark the point P where the other side of the 60°angle intersects the above perpendicular line.

To carry out this construction, follow these steps:

### Step-by-Step Construction:

1. **Draw a Line Segment MN**:
   - Using a ruler, draw a straight line segment \( MN \) of length 5 cm.

2. **Construct a 60° Angle at Point M**:
   - Place the compass at point \( M \), and set a convenient radius.
   - Draw an arc cutting \( MN \) and extending upwards.
   - Keep the same compass width, place the compass on the point where the arc cuts \( MN \), and draw a second arc cutting the first arc above \( M \).
   - Draw a straight line from \( M \) through the intersection of the arcs. This is the second arm of the 60° angle.

3. **Construct the Perpendicular at Point N**:
   - Place the compass at \( N \) and draw an arc intersecting the line \( MN \) at two points.
   - Keeping the same radius, place the compass on each intersection point, and draw two arcs above \( N \), making them intersect.
   - Draw a straight line through \( N \) and the intersection of these two arcs. This is the perpendicular line at \( N \).

4. **Mark the Point P**:
   - The point where the other side of the 60° angle intersects the perpendicular line from \( N \) is labeled as \( P \).

This completes the construction of the required geometrical figure.

### Do you want further details or have any questions?

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Here are 5 questions to deepen your understanding:
1. How would you construct a 90° angle at point M instead of 60°?
2. How can you verify that the constructed perpendicular line is accurate?
3. What happens if the angle at M is 45° instead of 60°?
4. How can you use a protractor to verify the angle you’ve constructed at M?
5. How would the construction change if the length of MN was different?

### Tip:
Always double-check your compass measurements to ensure the angles and perpendiculars are accurate.

Draw a straight line segment of length 5 cm and name MN. Construct an angle of 60° at M such that MN is an arm. Construct the perpendicular at point N. Mark the point P where the other side of the 60° angle intersects the above perpendicular line.

Learn step-by-step how to draw a 5 cm line segment MN, construct a 60° angle at M, and create a perpendicular at N. Mark the point P where the 60° angle intersects the perpendicular line. This geometry problem involves compass construction and basic theorems, suitable for Grades 6-8.

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