Constructing Perpendiculars from Point D to Sides AB and AC
To construct perpendiculars from point D to sides AB and AC in triangle ABC, follow these steps:
1. Draw Triangle ABC:
- Start by drawing triangle ABC on a piece of paper or a geometric software.
2. Locate Point D on Side BC:
- Choose a point D on side BC of triangle ABC.
3. Construct Perpendicular Line to Side AB:
- To construct a perpendicular line from point D to side AB, use a compass to draw an arc from point D to intersect side AB at point E.
- With the same compass width, draw arcs on either side of point D on side BC.
- Using a straightedge, draw a line passing through point E and perpendicular to side AB.
4. Construct Perpendicular Line to Side AC:
- To construct a perpendicular line from point D to side AC, repeat the same process as above.
- Use a compass to draw an arc from point D to intersect side AC at point F.
- Draw arcs on either side of point D on side BC.
- Draw a line passing through point F and perpendicular to side AC.
5. Verify Perpendicularity:
- To verify that the lines DE and DF are perpendicular to sides AB and AC, use a protractor to measure the angles formed at points E and F.
- A right angle measures 90 degrees, confirming that the lines are perpendicular to the respective sides.
By following these steps, you can successfully construct perpendiculars from point D to sides AB and AC in triangle ABC.

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