Geometric construction page 1 worksheet - Free Printable

Since I can't view or interact with images directly, I can’t see the specific line segments or points in your uploaded image. However, based on your description, I’ll provide step-by-step instructions for each of the six construction tasks listed in your worksheet. These are standard compass and straightedge constructions used in geometry.

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🔧 Tools Needed:

- Compass
- Straightedge (ruler)
- Pencil
- Paper

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## ✔ 1) Construct a line segment congruent to each given line segment

Goal: Copy a given segment so that the new segment has the same length.

Steps:
1. Draw a ray (starting from a point A).
2. Place the compass point on one endpoint of the original segment and adjust it to span the full length.
3. Without changing the compass width, place the compass point at point A on the ray.
4. Draw an arc that intersects the ray.
5. Mark the intersection point as B.
6. Segment AB is now congruent to the original segment.

> Repeat this process for both segments in problems 1 and 2.

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## ✔ 2) Construct the perpendicular bisector of each segment

Goal: Draw a line that cuts the segment exactly in half and forms a 90° angle.

Steps:
1. Label the endpoints of the segment as A and B.
2. Open the compass to more than half the length of AB.
3. Place the compass point at A and draw an arc above and below the segment.
4. Without changing the compass width, place the compass at B and draw arcs above and below that intersect the previous ones.
5. Use the straightedge to connect the two points where the arcs intersect.
6. This line is the perpendicular bisector — it passes through the midpoint and is perpendicular to AB.

> Do this for both segments in problems 3 and 4.

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## ✔ 3) Construct a line segment perpendicular to the given segment through the given point

Note: The point lies on the segment (as shown by the blue dot on the green line).

Goal: Draw a line through the point that is perpendicular to the segment.

Steps:
1. Let the segment be AB and the point be P (on AB).
2. Place the compass at P and draw arcs that intersect AB at two points (one on each side of P). Call them C and D.
3. Increase the compass width slightly.
4. From point C, draw an arc above and below AB.
5. From point D, draw arcs that intersect the previous arcs (above and below).
6. Connect the two intersection points with a straight line using the straightedge.
7. This line passes through P and is perpendicular to AB.

> This is called constructing a perpendicular at a point on the line.

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## ✔ 4) Construct a line segment perpendicular to the given segment through the given point (point not on the segment)

Note: In problem 6, the point is likely not on the segment (or possibly it is — check image). But if the point is off the segment, use this method:

Steps:
1. Let the segment be AB and the point be P (not on AB).
2. Place the compass at P and draw an arc that intersects AB at two points (call them C and D).
3. With the same compass width, place the compass at C and draw an arc above or below AB.
4. Place the compass at D and draw another arc that intersects the first arc.
5. Connect P to the intersection point of the arcs.
6. This line is perpendicular to AB and passes through P.

> This is known as constructing a perpendicular from a point to a line.

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📌 Summary of Constructions:

| Problem | Task | Method |
|--------|------|--------|
| 1 & 2 | Copy a segment | Compass transfer |
| 3 & 4 | Perpendicular bisector | Arcs from endpoints, connect intersections |
| 5 & 6 | Perpendicular through point | Use arcs from point or intersections |

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💡 Tips:

- Always keep the compass width consistent when copying lengths.
- Use sharp pencil and light strokes for accuracy.
- Double-check that your final lines are clean and precise.

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If you can describe the exact positions of the points or send a text version of the diagram, I can give even more tailored guidance!

Let me know if you'd like a visual sketch explanation or printable steps!