The purpose of today's block was to discover almost all of the necessary properties of chords, angles, and arc that are part of the circle unit.
There will be a quiz on Thurs-Fri this week over missing information related to circle properties - 24 pts
We warmed up with a quick fill-in-the-blank based on recently written Geometric Truth. Then students did an investigation (attached below) over C-76-80 on pp 459-60.
If you have congruent chords in a circle, then the corresponding central angles are congruent (C-76) and the intercepted arcs are congruent (C-77). The perpendicular from the center to a chord is a bisector of the chord (C-78). Congruent Chords are equidistant from the center of the circle (C-79). AND If you construct the perpendicular bisector of any chord, it will pass through the center of the circle (C-80, the converse of C-78).
A grade was taken over HW #6 and the new entries to Geometric Truth (6 pts). In 6th, a grade was taken over HW #5 (Aspire practice) - 4 pts.
Students practiced C-76-80 application by starting p 461:1-12. Most did not finish in class.
We also did Geogebra investigations of Conjectures 81-84. Those are attached below, with answers.
HW #7: finish p 461:1-12. Give conjecture number that helped you decide. Then do p 468:1-16, also giving conjecture number(s) that helped you decide.
Finish Geometric Truth entries for C-76 - 84, using class activities and notes to create good sketches for the conjectures.
Upcoming: Quiz Thurs-Fri, 9.1-3 - 24 pts. Circle Unit Test will be Thurs (0B), April 25 - Mon, April 29 (6th).
You need Geogebra as an APP on your device in order to open the .ggb files. I recommend opening on a computer.
Recommend for HW #7: print off p 468 and enlarge it a bit. Highlight intercepted arcs as you are working. Remember that each angle of the inscribed quadrilateral is also an inscribed angle with its own (very large sometimes) intercepted arc.
There will be a quiz on Thurs-Fri this week over missing information related to circle properties - 24 pts
We warmed up with a quick fill-in-the-blank based on recently written Geometric Truth. Then students did an investigation (attached below) over C-76-80 on pp 459-60.
If you have congruent chords in a circle, then the corresponding central angles are congruent (C-76) and the intercepted arcs are congruent (C-77). The perpendicular from the center to a chord is a bisector of the chord (C-78). Congruent Chords are equidistant from the center of the circle (C-79). AND If you construct the perpendicular bisector of any chord, it will pass through the center of the circle (C-80, the converse of C-78).
A grade was taken over HW #6 and the new entries to Geometric Truth (6 pts). In 6th, a grade was taken over HW #5 (Aspire practice) - 4 pts.
Students practiced C-76-80 application by starting p 461:1-12. Most did not finish in class.
We also did Geogebra investigations of Conjectures 81-84. Those are attached below, with answers.
HW #7: finish p 461:1-12. Give conjecture number that helped you decide. Then do p 468:1-16, also giving conjecture number(s) that helped you decide.
Finish Geometric Truth entries for C-76 - 84, using class activities and notes to create good sketches for the conjectures.
Upcoming: Quiz Thurs-Fri, 9.1-3 - 24 pts. Circle Unit Test will be Thurs (0B), April 25 - Mon, April 29 (6th).
You need Geogebra as an APP on your device in order to open the .ggb files. I recommend opening on a computer.
Recommend for HW #7: print off p 468 and enlarge it a bit. Highlight intercepted arcs as you are working. Remember that each angle of the inscribed quadrilateral is also an inscribed angle with its own (very large sometimes) intercepted arc.
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C 82-84.ggb |
c-81.ggb |