Unit 9 Toolbox
By Samuel Morey
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Last updated over 3 years ago
13 Questions
IMPORTANT TERMS
A circle is the set of all points that are equidistant from the center. Circles are named by their centers.
A tangent is a LINE that intersects the circle at ONE point.
A secant is a LINE that intersects the circle at TWO points.
A chord is a SEGMENT that intersects the circle at TWO points.
A diameter is a CHORD that contains the center of the circle.
An arc contains points on the circle and can be measured by its rotation(degrees) or length(cm, in, mi . . .etc).
Notice that minor arcs are named with 2 points on the circle and major arcs and semicircles are named with 3 points on the circle.
From p. 455 in your online textbook:
Circles can be tangent to each other if they share a single point.
An intercepted arc is an arc that lies in the interior of the angle with endpoints that lie on the sides of the angle.
A cyclic quadrilateral is a quadrilateral whose vertices all lie on the circle.
Refer to the GeoGebra investigation Tangent Properties to answer #1-3.
https://www.geogebra.org/m/kpffjt3r#chapter/601479
Choose the correct term of phrase to fill in the blank and then draw a figure that represents each conjecture in the Show Your Work section.
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1.
Tangent ConjectureA tangent to a circle is ______________________ to the radius drawn to the points of tangency.
Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.
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2.
Tangent Segments ConjectureTangent segments to a circle from a point outside the circle are ______________________.
Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.
Refer to the GeoGebra Chord Properties investigation to answer questions #3-4.
https://www.geogebra.org/m/kpffjt3r#chapter/601480
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3.
Chord Central Angles ConjectureIf two chords in a circle are congruent, then they determine two central angles that are _________________.
Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.
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4.
Chord Arcs ConjectureIf two chords in a circle are congruent, then their intercepted arcs are____________________.
Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.
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5.
Perpendicular to a Chord ConjectureThe perpendicular from the center of a circle to a chord is ____________________ of the chord.
Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.
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6.
Perpendicular Bisector of a Chord ConjectureThe perpendicular bisector of a chord passes through the ___________________of the circle.
Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.
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7.
Chord Distance to Center ConjectureTwo congruent chords in a circle are ________________________ from the center of the circle.
Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.
Refer to the GeoGebra Arcs and Angles investigation to answer #8-12.
https://www.geogebra.org/m/kpffjt3r#chapter/601481
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8.
Inscribed Angle ConjectureThe measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.
Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.
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9.
Inscribed Angles Intercepting Arcs ConjectureInscribed angles that intercept the same arc are_________________.
Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.
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10.
Angles Inscribed in a Semicircle ConjectureAngles inscribed in a semi-circle are __________________.
Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.
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11.
Parallel Lines Intercepted Arcs ConjectureParallel lines intercept _______________________ arcs on a circle.
Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.
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12.
Cyclic Quadrilateral ConjectureThe opposite angles of a cyclic quadrilateral are __________________.
Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.
Refer to the GeoGebra Arc Length investigation to answer question #13.
https://www.geogebra.org/m/kpffjt3r#material/rxsycvqc
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13.
Arc Length ConjectureThe length of an arc is equal to _____________________. Please label theta and r on your figure in the Show Your Work section.
Arc Length Conjecture
The length of an arc is equal to _____________________.
Please label theta and r on your figure in the Show Your Work section.