To solve this problem, you can use GeoGebra's tools to visualize and measure the segments AC and BC.

Here's the step-by-step process:

Step 1: Draw the perpendicular line

• In GeoGebra, use the "Perpendicular Line" tool to draw the line $CD \perp AB$. This will create the intersection, ensuring that line CD is perpendicular to the line AB.

Step 2: Draw the segments AC and BC

• Select the "Segment" tool in GeoGebra.
• Draw a segment from point A to point C, denoted as $AC$.
• Similarly, draw a segment from point B to point C, denoted as $BC$.

Step 3: Measure the lengths of AC and BC

• Use the "Distance or Length" tool in GeoGebra to measure the lengths of $AC$ and $BC$.
• Simply click on the segment $AC$, and the length will be displayed. Do the same for segment $BC$.

Step 4: Compare the lengths

• After measuring the lengths of both segments, observe how they compare.

Depending on the specific points A, B, and C, the lengths of AC and BC may or may not be equal. If point C is equidistant from A and B on line $AB$, then the lengths will be equal. Otherwise, they will differ.

Would you like to dive deeper into this, or do you have any specific questions about these steps?

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5 Related Questions:

1. What properties of perpendicular lines are relevant in this problem?
2. How can you use the Pythagorean Theorem if additional coordinates are provided?
3. How would the result change if CD were not perpendicular to AB?
4. Can you explore how changes in the position of point C affect the lengths of AC and BC?
5. How does symmetry around line AB influence the segment lengths?

Tip:

In GeoGebra, you can also use the "Midpoint" tool to check if C lies exactly in the middle of A and B. If so, $AC = BC$.