Chord Properties

Today we will start with some vocabulary and then introduce the properties of chords.

Some vocabulary will be a review and other terms will be new. Have your circle notes out so you can add to them!

Central Angle

What is the definition of a central angle? *hint: these are in your circle vocab notes already*

A line segment from the center of a circle[br]or sphere to a point on the circle or sphere. Also,[br]the length of that line segment. A line segment whose endpoints lie on a[br]circle. An angle whose vertex is the center[br]of a circle and whose sides pass through the[br]endpoints of an arc

Arc Measure

What is the definition of an arc measure?

The set of all points in a plane at a given distance from a given point The measure of the central angle that intercepts an arc, measured in degrees. An arc of a circle whose endpoints are the endpoints of a diameter

How many degrees are in a circle?

540 degrees 180 degrees 360 degrees

Inscribed Angle

What is the definition of an inscribed angle?

An angle whose vertex lies on a circle and whose sides are chords of the circle. An angle whose vertex is the center of a circle and whose sides pass through the endpoints of an arc. A line segment whose endpoints lie on a circle.

Intercepted Arc

Based on the picture above what do you think the definition of intercepted arc is?

A line that intersects a circle in two points. An arc that lies in the interior of an angle with endpoints on the sides of the angle. A line that lies in the plane of a circle and[br]that intersects the circle at exactly one point.

In this lesson you will discover some properties of chords, arcs, and central angles

[b]Chord Central Angles Conjecture:[/b] If two chords in a circle are congruent, then they determine two central angles that are ___________.

Congruent Supplementary Complementary

In this lesson you will discover some properties of chords, arcs, and central angles

[b]Chord Arcs Conjecture[/b]: If two chords in a circle are congruent, then their _________________ are congruent.

central angles intercepted arcs inscribed arcs

[img width=573,height=172]https://lh5.googleusercontent.com/4vacz2EzsJTY_YtECBjAma3kh9PdBILfXfuHrVcaEsq-i2VymGUEV1frsORhhp9Zb02Fwhi2OBnVTXlSDZTm3xrdjQQxlrZQWg2HQLlSBzQqemRjH4AHOuqCPajmexJlaOOTXUxR[/img]

[math]90^\circ[/math] [math]360^\circ[/math] [math]60^\circ[/math] [math]30^\circ[/math]

[img width=581,height=155]https://lh4.googleusercontent.com/yd6j5atkeRxoXjAiC_3N3qf5W5y-v3Bq3HdMPgKHxoURM12jnlWLXgedzUc1Mt1B7UuRPN3Fhg2IkuYs7XIM6TsPWEEh1rKa36htDp2FALNa2A7x8TIiMFgU_Jm48aUjzQFAxgTc[/img]

[math]150\degree[/math] [math]60^\circ[/math] [math]90^\circ[/math] [math]30^\circ[/math]

What is the value of w?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img005.png[/img]

140 degrees 70 degrees 180 degrees

[b]Perpendicular to a Chord Conjecture: [/b]The perpendicular from the center of a circle to a chord is the ________ of the chord.

angle bisector endpoint

[b]Chord Distance to Center Conjecture:[/b] Two congruent chords in a circle are ____________ from the center of the circle.

equidistant equiangular different distances

[img width=143,height=189]https://lh5.googleusercontent.com/5TFx52LhZ1WYC6fkGbLlZeOiishzN-JCXZC7arm-RFkkaNVltXDRx1xjlrDwEOQMRRPymZFaCSmjce7jEGQLNp-UCZI0IeEh7CiBDMT6Il4mv2a7nI-sY9LfAxQGUALHtlj7r_0X[/img]

8 cm 9 cm 6 cm

What is the value of z?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img004.png[/img]

212 degrees 84 degrees 32 degrees

What is the value of w?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img008.png[/img]

115 degrees 90 degrees 360 degrees

What is the value of x?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img008.png[/img]

115 degrees 360 degrees 90 degrees

What is the value of y?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img008.png[/img]

130 degrees 65 degrees 115 degrees

What's wrong with this picture?[br][img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg461-img005.png[/img]

What are the values of w, x, y & z?

the measure of arc AC is 130 degrees,[img]http://dg5.kendallhunt.com/khreader/kh_book/pages/images/ch09-se-pg462-img002.png[/img]

Chord Properties

Today we will start with some vocabulary and then introduce the properties of chords.

Central Angle

Arc Measure

Inscribed Angle

Intercepted Arc

In this lesson you will discover some properties of chords, arcs, and central angles

In this lesson you will discover some properties of chords, arcs, and central angles

What are the values of w, x, y & z?

Information: Chord Properties