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Notes, handouts, homework, and answers...all the stuff for 3/7

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7.1 practice 18-28 even, 34,36
7.2 practice 16-21 Identify transformations only, 28-30, 32

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problems numbers 5-30 all

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3/11

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And solutions

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Review of linear equations

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2.4 HW key

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Parallel and Perpendicular Lines

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8/26-8/27

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Don't Forget Delta Math!!!

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9/16

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9/16

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9/17

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11/18

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11/30 Properties

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12/1 Equations

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Remind is important
code: 8r33z3

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#s 13-21 odd on this page and 22-32 all on the next page

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Quiz moved to Friday.

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10/25

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10/25

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10/29

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10/29

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8.3 Simplify, Multiply, Divide Rational Expressions Notes &HW   3/30

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8.3 Simplify, Multiply, Divide Rational Expressions Notes &HW   3/30

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10/31

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10/31

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11/1

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and solutions

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8.4 Notes Add/subtract Rational Expressions & worksheet 3/31

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8.4 Notes Add/subtract Rational Expressions & worksheet 3/31

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11/4

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8.4 Practice worksheet solutions (odd) 3/31

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8.4 Practice worksheet solutions (odd) 3/31

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11/4

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Extra Adding/Subttaction Practice for the needy (with answers)

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Extra Adding/Subttaction Practice for the needy (with answers)

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11/19

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Notes and homework

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Properties of Parallelograms: Guided Notes

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Properties of Parallelograms: Guided Notes

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These are blank, so if you are absent, you must get the answers from a peer in class upon your return.

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and check out the quiz at the end to see if you get it!

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Some interesting things about angles and circles

Inscribed Angle

First off, a definition:

Inscribed Angle: an angle made from points sitting on the circle's circumference.

A and C are "end points"

B is the "apex point"

Play with it here:

images/circle-prop.js?mode=inscribe

When you move point "B", what happens to the angle?

Inscribed Angle Theorems

Keeping the end points fixed ...

... the angle a° is always the same,
no matter where it is on the same arc between end points:

(Called the Angles Subtended by Same Arc Theorem)

And an inscribed angle a° is half of the central angle 2a°

(Called the Angle at the Center Theorem)

Try it here (not always exact due to rounding):

images/circle-prop.js?mode=inscribe2

Example: What is the size of Angle POQ? (O is circle's center)

Angle POQ = 2 × Angle PRQ = 2 × 62° = 124°

Example: What is the size of Angle CBX?

Angle ADB = 32° also equals Angle ACB.

And Angle ACB also equals Angle XCB.

So in triangle BXC we know Angle BXC = 85°, and Angle XCB = 32°

Now use angles of a triangle add to 180° :

Angle CBX + 85° + 32° = 180°

Angle in a Semicircle (Thales' Theorem)

An angle inscribed across a circle's diameter is always a right angle:

(The end points are either end of a circle's diameter,
the apex point can be anywhere on the circumference.)

Play with it here:

images/circle-prop.js?mode=thales

Why? Because:

The inscribed angle 90° is half of the central angle 180°

(Using "Angle at the Center Theorem" above)

Another Good Reason Why It Works

We could also rotate the shape around 180° to make a rectangle!

It is a rectangle, because all sides are parallel, and both diagonals are equal.

And so its internal angles are all right angles (90°).

Example: What is the size of Angle BAC?

The Angle in the Semicircle Theorem tells us that Angle ACB = 90°

Now use angles of a triangle add to 180° to find Angle BAC:

Angle BAC + 55° + 90° = 180°

So there we go! No matter where that angle is
on the circumference, it is always 90°

Finding a Circle's Center

We can use this idea to find a circle's center:

draw a right angle from anywhere on the circle's circumference, then draw the diameter where the two legs hit the circle

do that again but for a different diameter

Where the diameters cross is the center!

Drawing a Circle From 2 Opposite Points

When we know two opposite points on a circle we can draw that circle.

Put some pins or nails on those points and use a builder's square like this:

Cyclic Quadrilateral

A "Cyclic" Quadrilateral has every vertex on a circle's circumference:

A Cyclic Quadrilateral's opposite angles add to 180°:

a + c = 180°
b + d = 180°

Example: What is the size of Angle WXY?

Opposite angles of a cyclic quadrilateral add to 180°

Angle WZY + Angle WXY = 180°

Tangent Angle

A tangent line just touches a circle at one point.

It always forms a right angle with the circle's radius.

1012, 3240, 1013, 3241, 1014, 3242, 1015, 3243, 1016, 3244

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Some interesting things about angles and circles First off, a definition: Inscribed Angle: an angle made from points sitting on the circle's circumference. A and C are "end points" B is the "apex point" Play with it here: images/circle-prop.js?mode=inscribe When you move point "B", what happens to the angle?

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and solutions

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Join an activity with your class and find or create your own quizzes and flashcards.

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Quizizz: You’ve been invited to a Quizizz activity

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Join an activity with your class and find or create your own quizzes and flashcards.

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