March 02, 2017

Arcs and Chords part 1Unit 9 Lesson 3

"Mathematics is a game played according to certain simple rules with meaningless marks on paper."

- David Hilbert (he help significantly update our geometric system)

Note: he was a bit sarcastic at times. Another fun quote after learning that a student in his class had dropped the subject in order to become a poet. "Good," he said. "He did not have enough imagination to become a mathematician."

March 02, 2017

In circle A, chord BC cuts off two arcs, BC and BDC.

We say the minor arc, BC, is the arcof the chord BC (and vice versa)

March 02, 2017

Computer Activity #1

1. Go to my website (www.tinyurl.com/WrightGeometry)2. Scroll down to Unit 9, Lesson 3 and select the Congruent Chords Link.3. Answer the following questions

Use the green dots to change the chords and white dots to change the circle size. Try the “slide me” with several different arrangements

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March 02, 2017

Q1: In the same circle, what can we say about congruent chords? Q2: What can we say about the two circles? Why? Q3: What can we say about congruent chords in congruent circles?

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Q4: Will the converse be true; i.e. will congruent arcs form congruent chords? (Use the slider backwards)

Q5: Consider the picture below where two chords are congruent. Are the arcs congruent? Why?

March 02, 2017

In Extra Problem #1, we proved half of the activity (and half of thefollowing theorem)

Theorem 9-4

In the same circle (or congruent circles) two chords are congruent if andonly if their arcs are congruent.

March 02, 2017

Computer Activity #2

1. Go to my website (www.tinyurl.com/WrightGeometry)2. Scroll down to Unit 9, Lesson 3 and select the Radius and Chords Link.3. Answer the following questions

Use the blue dots to change the chord length and white dot to change the circle size. Try the “slide me” with several different arrangements

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March 02, 2017

Q1: The diameter/radius drawn is ______________ to the chord.

Q2: When this diameter is drawn, what happens to the chord?

March 02, 2017

Q3: When this diameter is drawn, what happens to the arc of the chord?

Q4: What would happen if the diameter is not perpendicular to the chord?

March 02, 2017

Theorem 9-5

A radius (or diameter) that is perpendicular to achord bisects the chord and its arc

March 02, 2017

Computer Activity #3

1. Go to my website (www.tinyurl.com/WrightGeometry)2. Scroll down to Unit 9, Lesson 3 and select the Equidistant Chords Link.3. Answer the following questions

Use the pink dots to move the chords, the blue slider to change the distance from the center, and white dot to change the circle size. Try the “slide me” with several different arrangements

March 02, 2017

March 02, 2017

Q1: The distance from a point to line is the _______________ segment. (hint: watch the angle being formed)

Q2: When two chords are equidistant from the center of the circle, then what can be said about the two chords?

March 02, 2017

Q3: In the circle draw two chords of different length.Are they equidistant to the center? If not, thenWhich one is closer to the center of the circle?

March 02, 2017

Theorem 9-6

In the same circle (or congruent circles) two chords are congruentif and only if they are equidistant from the center (or centers)

March 02, 2017

Example 1:

In circle O with radius 12 cm and chord RS 6 cm from O. Find RS.

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Example 2: Find EB.

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Example 3:

March 02, 2017

If a radius bisects a chord, does it have to bisect chord's arc?

March 02, 2017