Unit 9 Toolbox

IMPORTANT TERMS

A circle is the set of all points that are equidistant from the center. Circles are named by their centers.

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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).

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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.

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An intercepted arc is an arc that lies in the interior of the angle with endpoints that lie on the sides of the angle.

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A cyclic quadrilateral is a quadrilateral whose vertices all lie on the circle.

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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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Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.

parallel

perpendicular

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Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.

congruent

not congruent

Refer to the GeoGebra Chord Properties investigation to answer questions #3-4.

https://www.geogebra.org/m/kpffjt3r#chapter/601480

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Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.

congruent

not congruent

1

Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.

congruent

not congruent

1

Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.

not a bisector

a bisector

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Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.

center

endpoint

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Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.

equidistant

halfway

Refer to the GeoGebra Arcs and Angles investigation to answer #8-12.

https://www.geogebra.org/m/kpffjt3r#chapter/601481

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Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

half

equal to

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Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.

congruent

not congruent

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Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.

acute angles

right angles

obtuse angles

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Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.

congruent

unequal

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Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.

complementary

supplementary

congruent

Refer to the GeoGebra Arc Length investigation to answer question #13.

https://www.geogebra.org/m/kpffjt3r#material/rxsycvqc

1

Unit 9 Toolbox

Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.

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.

Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.

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.

Unit 9 Toolbox

Unit 9 Toolbox

Tangent ConjectureA tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments ConjectureTangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles ConjectureIf two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs ConjectureIf two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord ConjectureThe perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord ConjectureThe perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center ConjectureTwo congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle ConjectureThe measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs ConjectureInscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle ConjectureAngles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs ConjectureParallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral ConjectureThe opposite angles of a cyclic quadrilateral are __________________.

Arc Length ConjectureThe length of an arc is equal to _____________________. Please label theta and r on your figure in the Show Your Work section.

Tangent ConjectureA tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments ConjectureTangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles ConjectureIf two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs ConjectureIf two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord ConjectureThe perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord ConjectureThe perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center ConjectureTwo congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle ConjectureThe measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs ConjectureInscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle ConjectureAngles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs ConjectureParallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral ConjectureThe opposite angles of a cyclic quadrilateral are __________________.

Arc Length ConjectureThe length of an arc is equal to _____________________. Please label theta and r on your figure in the Show Your Work section.

Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.

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.

Tangent Conjecture
A tangent to a circle is ______________________ to the radius drawn to the points of tangency.

Tangent Segments Conjecture
Tangent segments to a circle from a point outside the circle are ______________________.

Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are _________________.

Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are____________________.

Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is ____________________ of the chord.

Perpendicular Bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the ___________________of the circle.

Chord Distance to Center Conjecture
Two congruent chords in a circle are ________________________ from the center of the circle.

Inscribed Angle Conjecture
The measure of the angle inscribed in a circle is ___________ the measure of the intercepted arc.

Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are_________________.

Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semi-circle are __________________.

Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept _______________________ arcs on a circle.

Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are __________________.

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.