1. Investigation 9.2 – Chord Properties You need: ruler, pencil, 2 printed circles or your own compass, glue stick
In class section, do the following:
Write a sentence to describe a perpendicular bisector of a segment, sketch and mark.
Copy (see C-7): The shortest _____ from a point to a line is along a perpendicular segment to the line.
In one of your circles, use a ruler to add two 5 cm chords that are not parallel.
Connect the endpoints of the chords to the center of the circle with dashed line segments.
What part of the circle are the 4 segments you just drew? Mark your sketch with appropriate congruence marks. What kind of triangles did you draw? Are they congruent?
The two vertex angles of the triangles are _______ angles of the circle. Write in your notes: The ________ angles of two congruent chords are congruent.
An arc measure is the same of the measure of its ________ angle, so what is true about the two arcs that are between your two congruent chords? Write: If two chords in a circle are congruent, then their intercepted ______ are congruent.
Measure to locate midpoints of your two chords and connect to center. Are these segments altitudes for your triangles? So they are perpendicular to the _______. Are these two segments congruent? Look back up at your response to the second bullet point. What do you now know about the distances from the chords to the center? So the chords are __________ from the center.
On your second circle, draw a chord. Then draw a perpendicular bisector of the chord. What point does it pass through? So the perpendicular bisector of a chord passes through the _______ of the circle. (C-80)
Now try problems 1-12 on pp in your in-class section of your notebook. Refer to C-76 to 80 on By number, which conjecture(s) did you use to answer the question, or which definition from G.T?