6.2 Investigation 2: Perpendiculars and Chords
6.2 Investigation 2: Perpendiculars and Chords
Investigation 2
Step 1: Construct a large circle. Mark the center. (Completed for you)
Step 2: Construct two nonparallel congruent chords that are not diameters. (Completed for you)
Step 3: Construct the perpendiculars from the center to each chord. Use the perpendicular from a point tool to do this. Click the center point and then the chord.
Step 4: Mark the points where the perpendiculars intersect the chords, label these points as and .
Step 5: For each chord, create the segments from and to the endpoints of each chord. You will end up creating four segments. By creating these segments, the lengths of the segments should come up.
Step 6: Move point around. What do you notice?
How does the perpendicular from the center of a circle to a chord divide the chord? State your observations as a conjecture.
Perpendiculars and Chords Conjecture
The perpendicular from the center of a circle to a chord is the _________________________ of the chord.
*Do the chords have to be congruent for this conjecture to be true?
Step 7: With your compass, compare the distances (measure along the perpendicular) from the center to the chords.
State your observations as the next conjecture.
Congruent Chords and Centers Conjecture
Two congruent chords in a circle are __________________________ from the center of the circle.