G.11 Inscribed quadrilaterals

Inscribed Angles (Quadrilaterals)

Vocab:

• Inscribed angle: When two lines connect one point on the surface of a circle with two other points on that circle

• Intercepted arc: an arc formed when one or two different chords or line segments cut across a circle

The Inscribed angle Theorem:

The measure of the inscribed angle is HALF the measure of the intercepted arc

Inscribed angles:

The measure of the inscribed angle is half the angle of the central angle (remember that central angles and intercepted arcs have the same measure).

Multiple Choice

What is the measure of the INTERCEPTED ARC?

• 72°

• 36°

• 30°

• 180°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 62°

• 124°

• 31°

• 180°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 324°

• 162°

• 81°

• 51°

Multiple Choice

What is the measure of the INSCRIBED ANGLE?

• 30°

• 50°

• 100°

• 60°

Multiple Choice

What is the value of x?

• 5

• -5

• -15

• -20

Multiple Choice

What is the value of x?

• 23

• 95

• 190

• 120

Draw

Find the measures of angles 1, 2, 3, and 4.

Inscribed Quadrilateral

All 4 angles of the quadrilateral are "inscribed" angles.

What's so special about inscribed quadrilaterals?

If a quadrilateral is inscribed in a circle, then both pairs of opposite angles are supplementary. (That means they add up to 180.)

Fill in the Blanks

Those last two problems were too easy.

Think about what equation would be needed to find the value of x in this problem.

Once you've found x, what about y?

Think about what equation would be needed to find the value of y in this problem.

How could you check to see if you're right?

What should both pairs of opposite angles add up to again?

Let's do one more together.

Find the measure of angles L and N.

Fill in the Blanks

Review

Some text here about the topic of discussion

Parts of Circle and Properties of Quadrilaterals

Multiple Choice

What is arc HCG?

• major arc

• Radius

• semicircle

• minor arc

Multiple Choice

What is arc DF?

• major arc

• Radius

• semicircle

• minor arc

Multiple Choice

What is DG?

• Secant

• Radius

• Chord

• Tangent

Multiple Choice

What is BJ?

• Secant

• Radius

• Chord

• Tangent

Multiple Choice

What is H?

• Point of Tangency

• Radius

• Circle

• Tangent

Multiple Choice

What is A?

• Point of Tangency

• Radius

• Circle

• Tangent

Multiple Choice

What is AF?

• Chord

• Radius

• Secant

• Tangent

Multiple Choice

What is BD?

• Chord

• Radius

• Secant

• Tangent

Multiple Choice

Name the circle part shown

• Diameter

• Chord

• Radius

• Tangent

Multiple Choice

Name the circle part shaded in green

• Radius

• Diameter

• Semi-circle

• Arc

Multiple Choice

Name the circle part shown

• Arc

• Sector

• Chord

• Radius

Multiple Choice

What is AB?

• diameter

• center

• circumference

• radius

Multiple Choice

What is CB?

• diameter

• center

• circumference

• radius

Multiple Choice

If the diameter of a circle is 10 cm, the radius is 5 cm.

• TRUE

• FALSE

Multiple Choice

The distance across a circle through the center is called the_______________.

• radius

• circumference

• diameter

• area

Multiple Choice

What is C?

• diameter

• centre

• circumference

• radius

Multiple Choice

A line segment that connects two points in a circle without passing through the centre

• Radius

• Sector

• Segment

• Chord

Multiple Choice

What is twice as long as a radius

• Center

• Diameter

• Tanget

• Arc

Multiple Choice

What is twice as long as a radius

• Center

• Diameter

• Tanget

• Arc

Inscribed Angles and Central Angles

Multiple Choice

What is m∠ACB?

• 67.5°

• 90°

• 22.5°

• 45°

Multiple Choice

What is the measure of angle Q?

• A

• B

• C

• D

Multiple Choice

What is the measure of angle U?

• A

• B

• C

• D

Multiple Choice

What is the measure of angle U?

• A

• B

• C

• D

Explanation Slide...

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Explanation Slide...

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​What is the value of a? How do you know.

​

What is the value of b? How do you know.​

Fill in the Blanks

Fill in the Blanks

Draw

Find the measures of angles 1, 2, 3, and 4.

​Look at how point A shifts. Do you think the previous formula about angle measures still applies? Why

Multiple Choice

What is the value of x?

• 75

• 90

• 150

• 180

Multiple Choice

What is the value of w?

• 75

• 90

• 105

• 180

Multiple Choice

What is the value of y?

• 75

• 150

• 105

• 210